Instructions

This file (hdat9600_final_assignment.Rmd) is the R Markdown document in which you need to complete your HDAT9600 final assignment. This assignment is assessed and will count for 30% of the total course marks. The assignment comprises two tasks worth 15 marks each. The first task will focus on logistic regression, and the second task will focus on survival analysis. There is no word limit, but a report of about 10 pages in length when printed (except that it will not be printed) is appropriate.

Don’t hesitate to ask the course convenor for help via OpenLearning. The course instructor are happy to point you in the right direction and to make suggestions, but they won’t, of course, complete your assignments for you!

Data for this assignment

The data used for this assignment consist of records from Intensive Care Unit (ICU) hospital stays in the USA. All patients were adults who were admitted for a wide variety of reasons. ICU stays of less than 48 hours have been excluded.

The source data for the assignment are data made freely available for the 2012 MIT PhysioNet/Computing for Cardiology Challenge. Details are provided here. Training Set A data have been used. The original data has been modified and assembled to suit the purpose of this assignment. While not required for the purposes of this assignment, full details of the preparatory work can be found in the hdat9600_final_assignment_data_preparation file.

The dataframe consists of 120 variables, which are defined as follows:

Patient Descriptor Variables

  • RecordID: a unique integer for each ICU stay
  • Age: years
  • Gender: male/female
  • Height: cm
  • ICUType: Coronary Care Unit; Cardiac Surgery Recovery Unit; Medical ICU; Surgical ICU
  • Length_of_stay: The number of days between the patient’s admission to the ICU and the end of hospitalisation
  • Survival: The number of days between ICU admission and death for patients who died
  • Outcome Variables

  • in_hospital_death: 0:survivor/1:died in-hospital this is the outcome variable for Task 1: Logistic Regression
  • Status: True/False this is the censoring variable for Task 2: Survival Analysis
  • Days: Length of survival (in days) this is the survival time variable for Task 2: Survival Analysis
  • Clinical Variables

    Use the hyperlinks below to find out more about the clinical meaning of each variable. The first two clinical variables are summary scores that are used to assess patient condition and risk.

  • SAPS-I score [Simplified Acute Physiological Score (Le Gall et al., 1984)]
  • SOFA score [Sequential Organ Failure Assessment (Ferreira et al., 2001)]
  • The following 36 clinical measures were assessed at multiple timepoints during each patient’s ICU stay. For each of the 36 clinical measures, you are given 3 summary variables: a) The minimum value during the first 24 hours in ICU (_min), b) The maximum value during the first 24 hours in ICU (_max), and c) The difference between the mean and the most extreme values during the first 24 hours in ICU (_diff). For example, for the clinical measure Cholesterol, these three variables are labelled ‘Cholesterol_min’, ‘Cholesterol_max’, and ‘Cholesterol_diff’.

  • Albumin (g/dL)
  • ALP [Alkaline phosphatase (IU/L)]
  • ALT [Alanine transaminase (IU/L)]
  • AST [Aspartate transaminase (IU/L)]
  • Bilirubin (mg/dL)
  • BUN [Blood urea nitrogen (mg/dL)]
  • Cholesterol (mg/dL)
  • Creatinine [Serum creatinine (mg/dL)]
  • DiasABP [Invasive diastolic arterial blood pressure (mmHg)]
  • FiO2 [Fractional inspired O2 (0-1)]
  • GCS [Glasgow Coma Score (3-15)]
  • Glucose [Serum glucose (mg/dL)]
  • HCO3 [Serum bicarbonate (mmol/L)]
  • HCT [Hematocrit (%)]
  • HR [Heart rate (bpm)]
  • K [Serum potassium (mEq/L)]
  • Lactate (mmol/L)
  • Mg [Serum magnesium (mmol/L)]
  • MAP [Invasive mean arterial blood pressure (mmHg)]
  • MechVent [Mechanical ventilation respiration (0:false, or 1:true)]
  • Na [Serum sodium (mEq/L)]
  • NIDiasABP [Non-invasive diastolic arterial blood pressure (mmHg)]
  • NIMAP [Non-invasive mean arterial blood pressure (mmHg)]
  • NISysABP [Non-invasive systolic arterial blood pressure (mmHg)]
  • PaCO2 [partial pressure of arterial CO2 (mmHg)]
  • PaO2 [Partial pressure of arterial O2 (mmHg)]
  • pH [Arterial pH (0-14)]
  • Platelets (cells/nL)
  • RespRate [Respiration rate (bpm)]
  • SaO2 [O2 saturation in hemoglobin (%)]
  • SysABP [Invasive systolic arterial blood pressure (mmHg)]
  • Temp [Temperature (°C)]
  • TropI [Troponin-I (μg/L)]
  • TropT [Troponin-T (μg/L)]
  • Urine [Urine output (mL)]
  • WBC [White blood cell count (cells/nL)]
  • Weight (kg)
  • Accessing the Data

    The data frame can be loaded with the following code:

    # Getting the path of your current open file
    # Extra code to ensure this file imports birth.csv in local directory for everyone
    library(rstudioapi)
    current_path <- rstudioapi::getActiveDocumentContext()$path 
    setwd(dirname(current_path ))
    
    icu_patients_df0 <- readRDS("icu_patients_df0.rds")
    icu_patients_df1 <- readRDS("icu_patients_df1.rds")

    Note: icu_patients_df1 is an imputed (i.e. missing values are ‘derived’) version of icu_patients_df0. This assignment does not concern the methods used for imputation.

    Task 1 (15 marks)

    In this task, you are required to develop a logistic regression model using the icu_patients_df1 data set which adequately explains or predicts the in_hospital_death variable as the outcome using a subset of the available predictor variables. You should fit a series of models, evaluating each one, before you present your final model. Your final model should not include all the predictor variables, just a small subset of them, which you have selected based on statistical significance and/or background knowledge. It is perfectly acceptable to include predictor variables in your final model which are not statistically significant, as long as you justify their inclusion on medical or physiological grounds (you will not be marked down if your medical justification is not exactly correct or complete, but do you best). Aim for between five and ten predictor variables (slightly more or fewer is OK). You should assess each model you consider for goodness of fit and other relevant statistics to help you choose between them. For your final model, present a set of diagnostic statistics and/or charts and comment on them. You don’t need to do an exhaustive exploratory data analysis of all the variables in the data set, but you should examine those variables that you use in your model. Finally, re-fit your final model to the unimputed data frame (icu_patients_df0.rds) and comment on any differences you find compared to the same model fitted to the imputed data.

    Hints

    1. Select an initial subset of explanatory variables that you will use to predict the risk of in-hospital death. Justify your choice.

    **Selecting an initial subset of explanatory variables:

    To select a subset of explanatory variables our group of investigators will examine the SAPS1 score and the SOFA score included in the dataset in more detail to ascertain the variables that might be logically associated with increased mortality and poor survival. We will also assess the APACHE score which is commonly used in ICU risk predcition models.

    SAPS1 - Simplified Acute Physiology Score is a measure of the severity of disease for patients admitted to ICU. The following measures increases the SAPS1 score:

    • Advanced Age
    • Low and high Heart Rate
    • Low and high Systolic Blood Pressure
    • High Temperature
    • Low Glasgow Coma Scale (However it is most meaningful to use the highest GCS score available for prognostication)
    • Mechanical Ventilation or CPAP
    • High PaO2/ FiO2 ratio (It is likely that highes FiO2 is administered during lowest PaO2)
    • Low Urine Output
    • High Blood Urea Nitrogen
    • Low or High Sodium
    • Low or high Potassium
    • Low Bicarbonate
    • High Bilirubin
    • Low or High White Blood Cell
    • Chronic diseases
    • Type of admission (ie ICU Type)

    SOFA - sequential organ failure assessment is a predictor of ICU mortality. The following measures increase the SOFA score: Elevated PaO2/ FiO2 ratio- * Reduced GCS - Nervous system * Reduced MAP - Cardiovascular system * Administration of vasopressors - Cardiovascular system * High Bilirubin - Liver * Low Platelets - Coagulation * High Creatinine - Kidneys * Low Urine - Kidneys

    *The APACHE score is commonly used validated risk score for ICU risk prediction. The variables that increase the APACHE score include:

    • Advanced Age

    • High or Low Temperature

    • High or Low MAP

    • High or Low HR

    • High or Low Respiratory Rate

    • High PaO2/FiO2 ratio

    • High or Low pH

    • High or Low Na

    • High or Low K

    • High Creatinine

    • High or low HCT

    • High or Low WBC

    • For our analysis, we will include variables that will increase SOFA, SAPS or APACHE scores. eg: increased BUN and reduced HCO3 will increase the SAPS score, therfore we will include BUN max(but not BUN_min and BUN_diff) and HCO3_min (but not HCO3_max and HCO3_diff). Where both extremes of a variable will increase the risk score, both min and max variables will be included.

    • Other factors known to be associated with morbidity/ mortality not included in risk scores:

      • Height/ weight - Body composition/ BMI is associated with mortality and survival
      • Gender - Male gender associated with worse outcomes
      • Glucose - high and low Glucose levels are associated with pathology
      • Troponin T and I - high troponin results(cardiac biomarkers) associated with morbidity and mortality
      • Lactate - elevated lactate is associated with poor organ perfusion and ICU morbidity/ mortality
      • Albumin - reduced albumin is associated with poor clinical outcomes

    BELOW IS A LIST OF THE VARIABLES TO BE INCLUDED: DEMOGRAPHIC VARAIBLES: * Age * Gender * ICU Type * Height * Weight_max

    CLINICAL VARIABLES: * Albumin_min * Bilirubin_max * BUN_max * Creatinine_max
    * GCS_min * Glucose_min and Glucose_max * HCO3_min * HR_min and HR_max * K_min K_max * Lactate_max * MAP_min
    * Na_min and Na_max * NISysABP_min and NISysABP_max * Platelets_min * FiO2_max and PaO2_min - included as PFratio: PaO2_min/ FiO2_max * pH_min and pH_max * RespRate_min and RespRate_max * Temp_min and Temp_max * TroponinI_max * TroponinT_max * Urine_min * WBC_min and WBC_max

    summary(icu_patients_df1)
    ##     RecordID      Length_of_stay       SAPS1            SOFA       
    ##  Min.   :132539   Min.   : -1.00   Min.   : 1.00   Min.   :-1.000  
    ##  1st Qu.:133875   1st Qu.:  6.00   1st Qu.:11.00   1st Qu.: 3.000  
    ##  Median :135146   Median : 10.00   Median :15.00   Median : 6.000  
    ##  Mean   :135156   Mean   : 13.74   Mean   :14.96   Mean   : 6.441  
    ##  3rd Qu.:136477   3rd Qu.: 17.00   3rd Qu.:19.00   3rd Qu.: 9.000  
    ##  Max.   :137740   Max.   :154.00   Max.   :34.00   Max.   :22.000  
    ##                                    NA's   :96                      
    ##     Survival      in_hospital_death      Days        Status       
    ##  Min.   :   0.0   Min.   :0.0000    Min.   :   0   Mode :logical  
    ##  1st Qu.:  10.0   1st Qu.:0.0000    1st Qu.: 265   FALSE:1288     
    ##  Median :  68.0   Median :0.0000    Median :2408   TRUE :773      
    ##  Mean   : 343.1   Mean   :0.1441    Mean   :1634                  
    ##  3rd Qu.: 420.0   3rd Qu.:0.0000    3rd Qu.:2408                  
    ##  Max.   :2408.0   Max.   :1.0000    Max.   :2408                  
    ##  NA's   :1288                                                     
    ##       Age         Albumin_diff      Albumin_max     Albumin_min   
    ##  Min.   :16.00   Min.   :0.01866   Min.   :1.100   Min.   :1.100  
    ##  1st Qu.:52.00   1st Qu.:0.28134   1st Qu.:2.600   1st Qu.:2.600  
    ##  Median :67.00   Median :0.48134   Median :3.000   Median :3.000  
    ##  Mean   :64.41   Mean   :0.56829   Mean   :3.045   Mean   :3.012  
    ##  3rd Qu.:78.00   3rd Qu.:0.81866   3rd Qu.:3.500   3rd Qu.:3.500  
    ##  Max.   :90.00   Max.   :2.31866   Max.   :5.300   Max.   :5.300  
    ##                                                                   
    ##     ALP_diff           ALP_max          ALP_min          ALT_diff        
    ##  Min.   :   0.148   Min.   :  19.0   Min.   :  19.0   Min.   :    0.446  
    ##  1st Qu.:  21.852   1st Qu.:  57.0   1st Qu.:  58.0   1st Qu.:   89.446  
    ##  Median :  37.852   Median :  78.0   Median :  76.0   Median :  102.446  
    ##  Mean   :  56.259   Mean   : 105.7   Mean   : 101.4   Mean   :  154.873  
    ##  3rd Qu.:  54.852   3rd Qu.: 110.0   3rd Qu.: 105.0   3rd Qu.:  108.446  
    ##  Max.   :1408.148   Max.   :1504.0   Max.   :1339.0   Max.   :10319.554  
    ##                                                                          
    ##     ALT_max           ALT_min          AST_diff            AST_max       
    ##  Min.   :    3.0   Min.   :   1.0   Min.   :    0.647   Min.   :    5.0  
    ##  1st Qu.:   17.0   1st Qu.:  17.0   1st Qu.:  123.353   1st Qu.:   27.0  
    ##  Median :   30.0   Median :  30.0   Median :  142.353   Median :   51.0  
    ##  Mean   :  118.3   Mean   :  90.1   Mean   :  227.991   Mean   :  188.1  
    ##  3rd Qu.:   69.0   3rd Qu.:  69.0   3rd Qu.:  152.353   3rd Qu.:  130.0  
    ##  Max.   :10440.0   Max.   :9240.0   Max.   :15870.647   Max.   :16040.0  
    ##                                                                          
    ##     AST_min       Bilirubin_diff     Bilirubin_max    Bilirubin_min   
    ##  Min.   :   5.0   Min.   : 0.03596   Min.   : 0.100   Min.   : 0.100  
    ##  1st Qu.:  24.0   1st Qu.: 1.06404   1st Qu.: 0.400   1st Qu.: 0.400  
    ##  Median :  42.0   Median : 1.36404   Median : 0.700   Median : 0.600  
    ##  Mean   : 116.4   Mean   : 1.97637   Mean   : 1.739   Mean   : 1.568  
    ##  3rd Qu.:  87.0   3rd Qu.: 1.46404   3rd Qu.: 1.300   3rd Qu.: 1.100  
    ##  Max.   :7960.0   Max.   :44.13596   Max.   :45.900   Max.   :45.500  
    ##                                                                       
    ##     BUN_diff           BUN_max          BUN_min       Cholesterol_diff  
    ##  Min.   :  0.4729   Min.   :  3.00   Min.   :  2.00   Min.   :  0.5772  
    ##  1st Qu.:  7.4729   1st Qu.: 14.00   1st Qu.: 12.00   1st Qu.: 17.5772  
    ##  Median : 11.5270   Median : 20.00   Median : 18.00   Median : 34.4228  
    ##  Mean   : 15.7904   Mean   : 27.48   Mean   : 24.44   Mean   : 37.2723  
    ##  3rd Qu.: 16.5270   3rd Qu.: 33.00   3rd Qu.: 29.00   3rd Qu.: 55.4228  
    ##  Max.   :172.4729   Max.   :197.00   Max.   :157.00   Max.   :173.5772  
    ##                                                                         
    ##  Cholesterol_max Cholesterol_min Creatinine_diff    Creatinine_max  
    ##  Min.   : 59.0   Min.   : 59     Min.   : 0.03245   Min.   : 0.200  
    ##  1st Qu.:122.0   1st Qu.:121     1st Qu.: 0.33245   1st Qu.: 0.800  
    ##  Median :152.0   Median :152     Median : 0.53245   Median : 1.000  
    ##  Mean   :153.4   Mean   :153     Mean   : 0.86298   Mean   : 1.499  
    ##  3rd Qu.:181.0   3rd Qu.:179     3rd Qu.: 0.73245   3rd Qu.: 1.500  
    ##  Max.   :330.0   Max.   :330     Max.   :20.76755   Max.   :22.000  
    ##                                                                     
    ##  Creatinine_min    DiasABP_diff       DiasABP_max      DiasABP_min    
    ##  Min.   : 0.200   Min.   :  0.5442   Min.   : 22.00   Min.   :  2.00  
    ##  1st Qu.: 0.700   1st Qu.: 16.5442   1st Qu.: 68.00   1st Qu.: 40.00  
    ##  Median : 0.900   Median : 21.5442   Median : 77.00   Median : 46.00  
    ##  Mean   : 1.319   Mean   : 24.5299   Mean   : 78.24   Mean   : 46.56  
    ##  3rd Qu.: 1.300   3rd Qu.: 28.4558   3rd Qu.: 86.00   3rd Qu.: 52.00  
    ##  Max.   :14.100   Max.   :209.4558   Max.   :268.00   Max.   :258.00  
    ##                   NA's   :715        NA's   :715      NA's   :715     
    ##    FiO2_diff          FiO2_max         FiO2_min         GCS_diff    
    ##  Min.   :0.00192   Min.   :0.2800   Min.   :0.2800   Min.   :0.244  
    ##  1st Qu.:0.15192   1st Qu.:0.5000   1st Qu.:0.4000   1st Qu.:3.756  
    ##  Median :0.44808   Median :1.0000   Median :0.4000   Median :3.756  
    ##  Mean   :0.31376   Mean   :0.7874   Mean   :0.4863   Mean   :5.183  
    ##  3rd Qu.:0.44808   3rd Qu.:1.0000   3rd Qu.:0.5000   3rd Qu.:8.244  
    ##  Max.   :0.44808   Max.   :1.0000   Max.   :1.0000   Max.   :8.244  
    ##                                                                     
    ##     GCS_max         GCS_min          Gender      Glucose_diff      
    ##  Min.   : 3.00   Min.   : 3.000   Female: 913   Min.   :   0.1445  
    ##  1st Qu.:11.00   1st Qu.: 3.000   Male  :1148   1st Qu.:  23.8555  
    ##  Median :15.00   Median : 8.000                 Median :  39.1445  
    ##  Mean   :12.87   Mean   : 8.773                 Mean   :  57.0844  
    ##  3rd Qu.:15.00   3rd Qu.:14.000                 3rd Qu.:  61.8555  
    ##  Max.   :15.00   Max.   :15.000                 Max.   :1003.1445  
    ##                                                                    
    ##   Glucose_max      Glucose_min      HCO3_diff          HCO3_max    
    ##  Min.   :  39.0   Min.   : 24.0   Min.   : 0.2275   Min.   : 9.00  
    ##  1st Qu.: 117.0   1st Qu.: 98.0   1st Qu.: 1.7725   1st Qu.:22.00  
    ##  Median : 141.0   Median :117.0   Median : 3.2275   Median :24.00  
    ##  Mean   : 163.3   Mean   :124.8   Mean   : 4.1506   Mean   :24.27  
    ##  3rd Qu.: 180.0   3rd Qu.:141.0   3rd Qu.: 5.2275   3rd Qu.:27.00  
    ##  Max.   :1143.0   Max.   :632.0   Max.   :24.2275   Max.   :47.00  
    ##                                                                    
    ##     HCO3_min        HCT_diff           HCT_max         HCT_min     
    ##  Min.   : 5.00   Min.   : 0.06013   Min.   :21.20   Min.   : 9.00  
    ##  1st Qu.:20.00   1st Qu.: 2.96013   1st Qu.:30.00   1st Qu.:26.20  
    ##  Median :23.00   Median : 5.16013   Median :33.10   Median :29.60  
    ##  Mean   :22.43   Mean   : 5.70366   Mean   :33.57   Mean   :30.08  
    ##  3rd Qu.:25.00   3rd Qu.: 7.66013   3rd Qu.:36.70   3rd Qu.:33.70  
    ##  Max.   :44.00   Max.   :23.43987   Max.   :54.40   Max.   :50.60  
    ##                                                                    
    ##      Height         HR_diff             HR_max          HR_min      
    ##  Min.   : 13.0   Min.   :  0.9221   Min.   : 44.0   Min.   :  0.00  
    ##  1st Qu.:162.6   1st Qu.: 20.0779   1st Qu.: 91.0   1st Qu.: 61.00  
    ##  Median :170.2   Median : 27.0779   Median :104.0   Median : 71.00  
    ##  Mean   :170.0   Mean   : 30.4294   Mean   :106.6   Mean   : 71.99  
    ##  3rd Qu.:177.8   3rd Qu.: 36.9221   3rd Qu.:119.0   3rd Qu.: 81.00  
    ##  Max.   :426.7   Max.   :212.9221   Max.   :300.0   Max.   :126.00  
    ##  NA's   :992                                                        
    ##                           ICUType        K_diff             K_max       
    ##  Coronary Care Unit           :297   Min.   : 0.03521   Min.   : 2.500  
    ##  Cardiac Surgery Recovery Unit:448   1st Qu.: 0.33521   1st Qu.: 4.000  
    ##  Medical ICU                  :788   Median : 0.56479   Median : 4.300  
    ##  Surgical ICU                 :528   Mean   : 0.69010   Mean   : 4.419  
    ##                                      3rd Qu.: 0.86479   3rd Qu.: 4.700  
    ##                                      Max.   :18.76479   Max.   :22.900  
    ##                                                                         
    ##      K_min       Lactate_diff        Lactate_max      Lactate_min    
    ##  Min.   :1.80   Min.   : 0.003596   Min.   : 0.400   Min.   : 0.300  
    ##  1st Qu.:3.50   1st Qu.: 1.096404   1st Qu.: 1.500   1st Qu.: 1.200  
    ##  Median :3.90   Median : 1.503596   Median : 2.200   Median : 1.600  
    ##  Mean   :3.95   Mean   : 1.753380   Mean   : 2.773   Mean   : 1.899  
    ##  3rd Qu.:4.30   3rd Qu.: 1.896404   3rd Qu.: 3.200   3rd Qu.: 2.200  
    ##  Max.   :6.90   Max.   :26.503596   Max.   :29.300   Max.   :24.200  
    ##                                                                      
    ##     MAP_diff           MAP_max         MAP_min          Mg_diff      
    ##  Min.   :  0.2316   Min.   :  4.0   Min.   :  1.00   Min.   :0.0157  
    ##  1st Qu.: 21.7684   1st Qu.: 94.0   1st Qu.: 55.00   1st Qu.:0.1843  
    ##  Median : 29.2316   Median :104.0   Median : 61.00   Median :0.3157  
    ##  Mean   : 38.4735   Mean   :111.8   Mean   : 62.76   Mean   :0.4181  
    ##  3rd Qu.: 41.2316   3rd Qu.:117.0   3rd Qu.: 70.00   3rd Qu.:0.5843  
    ##  Max.   :213.2316   Max.   :291.0   Max.   :265.00   Max.   :7.9157  
    ##                                                                      
    ##      Mg_max          Mg_min         Na_diff            Na_max     
    ##  Min.   :1.100   Min.   :0.600   Min.   : 0.2066   Min.   :112.0  
    ##  1st Qu.:1.900   1st Qu.:1.600   1st Qu.: 1.7934   1st Qu.:137.0  
    ##  Median :2.100   Median :1.800   Median : 3.2066   Median :140.0  
    ##  Mean   :2.153   Mean   :1.857   Mean   : 4.1146   Mean   :139.8  
    ##  3rd Qu.:2.400   3rd Qu.:2.100   3rd Qu.: 5.2066   3rd Qu.:142.0  
    ##  Max.   :9.900   Max.   :6.200   Max.   :41.2066   Max.   :177.0  
    ##                                                                   
    ##      Na_min    NIDiasABP_diff    NIDiasABP_max    NIDiasABP_min  
    ##  Min.   : 98   Min.   :  0.491   Min.   : 29.00   Min.   :10.00  
    ##  1st Qu.:136   1st Qu.: 17.509   1st Qu.: 64.00   1st Qu.:33.00  
    ##  Median :138   Median : 25.500   Median : 76.00   Median :42.00  
    ##  Mean   :138   Mean   : 26.964   Mean   : 76.92   Mean   :43.17  
    ##  3rd Qu.:141   3rd Qu.: 33.509   3rd Qu.: 89.00   3rd Qu.:52.00  
    ##  Max.   :160   Max.   :116.509   Max.   :174.00   Max.   :97.00  
    ##                NA's   :455       NA's   :455      NA's   :455    
    ##    NIMAP_diff         NIMAP_max        NIMAP_min      NISysABP_diff     
    ##  Min.   :  0.0407   Min.   : 47.33   Min.   :  7.00   Min.   :  0.3013  
    ##  1st Qu.: 18.2893   1st Qu.: 81.08   1st Qu.: 52.33   1st Qu.: 25.6987  
    ##  Median : 24.7107   Median : 93.67   Median : 60.00   Median : 34.3013  
    ##  Mean   : 26.9759   Mean   : 94.47   Mean   : 61.69   Mean   : 37.7962  
    ##  3rd Qu.: 33.2893   3rd Qu.:106.00   3rd Qu.: 70.00   3rd Qu.: 45.6987  
    ##  Max.   :113.2893   Max.   :189.00   Max.   :121.00   Max.   :157.3013  
    ##  NA's   :455        NA's   :455      NA's   :455      NA's   :453       
    ##   NISysABP_max    NISysABP_min      PaCO2_diff        PaCO2_max    
    ##  Min.   : 78.0   Min.   :  4.00   Min.   : 0.3358   Min.   :16.00  
    ##  1st Qu.:121.0   1st Qu.: 83.00   1st Qu.: 5.6642   1st Qu.:39.00  
    ##  Median :138.0   Median : 95.00   Median : 8.6642   Median :44.00  
    ##  Mean   :140.5   Mean   : 96.55   Mean   :10.7463   Mean   :45.56  
    ##  3rd Qu.:156.0   3rd Qu.:108.00   3rd Qu.:13.3358   3rd Qu.:50.00  
    ##  Max.   :274.0   Max.   :234.00   Max.   :57.6642   Max.   :98.00  
    ##  NA's   :453     NA's   :453                                       
    ##    PaCO2_min       PaO2_diff           PaO2_max        PaO2_min    
    ##  Min.   : 0.30   Min.   :  0.6179   Min.   : 27.0   Min.   : 20.0  
    ##  1st Qu.:32.00   1st Qu.: 67.6179   1st Qu.:123.0   1st Qu.: 74.0  
    ##  Median :36.00   Median : 90.6179   Median :191.0   Median : 92.0  
    ##  Mean   :36.72   Mean   :119.5407   Mean   :223.5   Mean   :105.8  
    ##  3rd Qu.:40.00   3rd Qu.:154.3821   3rd Qu.:311.0   3rd Qu.:122.0  
    ##  Max.   :93.00   Max.   :341.3821   Max.   :500.0   Max.   :477.0  
    ##                                                                    
    ##     pH_diff             pH_max          pH_min      Platelets_diff    
    ##  Min.   :0.000114   Min.   :7.150   Min.   :3.000   Min.   :  0.2307  
    ##  1st Qu.:0.059886   1st Qu.:7.380   1st Qu.:7.280   1st Qu.: 39.7693  
    ##  Median :0.089886   Median :7.420   Median :7.340   Median : 72.7693  
    ##  Mean   :0.098486   Mean   :7.418   Mean   :7.327   Mean   : 92.5348  
    ##  3rd Qu.:0.120114   3rd Qu.:7.460   3rd Qu.:7.390   3rd Qu.:116.7693  
    ##  Max.   :4.369886   Max.   :7.690   Max.   :7.630   Max.   :857.2307  
    ##                                                                       
    ##  Platelets_max    Platelets_min   RespRate_diff      RespRate_max  
    ##  Min.   :  18.0   Min.   :  9.0   Min.   : 0.6514   Min.   :13.00  
    ##  1st Qu.: 157.0   1st Qu.:126.0   1st Qu.: 7.3486   1st Qu.:24.00  
    ##  Median : 210.0   Median :184.0   Median : 9.6514   Median :27.00  
    ##  Mean   : 228.9   Mean   :197.9   Mean   :11.6075   Mean   :29.12  
    ##  3rd Qu.: 275.0   3rd Qu.:246.0   3rd Qu.:13.6514   3rd Qu.:33.00  
    ##  Max.   :1047.0   Max.   :891.0   Max.   :78.6514   Max.   :98.00  
    ##                                                                    
    ##   RespRate_min     SaO2_diff          SaO2_max         SaO2_min     
    ##  Min.   : 4.00   Min.   : 0.2461   Min.   : 75.00   Min.   : 33.00  
    ##  1st Qu.:12.00   1st Qu.: 0.7539   1st Qu.: 97.00   1st Qu.: 95.00  
    ##  Median :14.00   Median : 1.7539   Median : 98.00   Median : 97.00  
    ##  Mean   :14.25   Mean   : 2.5635   Mean   : 97.44   Mean   : 95.85  
    ##  3rd Qu.:17.00   3rd Qu.: 3.2461   3rd Qu.: 99.00   3rd Qu.: 98.00  
    ##  Max.   :24.00   Max.   :64.2461   Max.   :100.00   Max.   :100.00  
    ##                                                                     
    ##   SysABP_diff        SysABP_max      SysABP_min       Temp_diff      
    ##  Min.   :  3.689   Min.   : 52.0   Min.   : 11.00   Min.   : 0.1259  
    ##  1st Qu.: 32.310   1st Qu.:135.0   1st Qu.: 79.00   1st Qu.: 0.8741  
    ##  Median : 40.690   Median :149.0   Median : 88.00   Median : 1.2741  
    ##  Mean   : 45.008   Mean   :152.1   Mean   : 90.91   Mean   : 1.3756  
    ##  3rd Qu.: 53.690   3rd Qu.:167.0   3rd Qu.:102.00   3rd Qu.: 1.7259  
    ##  Max.   :178.690   Max.   :295.0   Max.   :262.00   Max.   :12.7741  
    ##  NA's   :715       NA's   :715     NA's   :715                       
    ##     Temp_max        Temp_min     TroponinI_diff    TroponinI_max  
    ##  Min.   :35.40   Min.   :24.20   Min.   : 0.1571   Min.   : 0.30  
    ##  1st Qu.:37.10   1st Qu.:35.60   1st Qu.: 4.6429   1st Qu.: 2.60  
    ##  Median :37.60   Median :36.10   Median : 5.2571   Median : 7.80  
    ##  Mean   :37.69   Mean   :36.01   Mean   :10.1737   Mean   :11.83  
    ##  3rd Qu.:38.20   3rd Qu.:36.60   3rd Qu.:12.1571   3rd Qu.:17.60  
    ##  Max.   :42.10   Max.   :38.30   Max.   :37.9571   Max.   :43.40  
    ##                                                                   
    ##  TroponinI_min   TroponinT_diff    TroponinT_max     TroponinT_min    
    ##  Min.   : 0.30   Min.   : 0.0215   Min.   : 0.0100   Min.   : 0.0100  
    ##  1st Qu.: 1.30   1st Qu.: 0.5785   1st Qu.: 0.0600   1st Qu.: 0.0400  
    ##  Median : 6.80   Median : 0.6285   Median : 0.1700   Median : 0.1200  
    ##  Mean   :10.06   Mean   : 1.0920   Mean   : 0.9079   Mean   : 0.6347  
    ##  3rd Qu.:13.20   3rd Qu.: 0.6585   3rd Qu.: 0.8000   3rd Qu.: 0.4700  
    ##  Max.   :42.90   Max.   :23.7915   Max.   :24.4600   Max.   :22.9300  
    ##                                                                       
    ##    Urine_diff        Urine_max        Urine_min         WBC_diff        
    ##  Min.   :  19.22   Min.   :   0.0   Min.   :  0.00   Min.   :  0.03315  
    ##  1st Qu.: 100.78   1st Qu.: 200.0   1st Qu.:  0.00   1st Qu.:  2.63315  
    ##  Median : 300.78   Median : 400.0   Median : 20.00   Median :  4.53315  
    ##  Mean   : 438.25   Mean   : 521.8   Mean   : 34.55   Mean   :  5.82079  
    ##  3rd Qu.: 525.78   3rd Qu.: 625.0   3rd Qu.: 36.00   3rd Qu.:  7.23315  
    ##  Max.   :4900.78   Max.   :5000.0   Max.   :600.00   Max.   :143.46685  
    ##                                                                         
    ##     WBC_max          WBC_min        Weight_diff          Weight_max    
    ##  Min.   :  0.10   Min.   :  0.10   Min.   :  0.00012   Min.   : 34.60  
    ##  1st Qu.:  9.30   1st Qu.:  7.60   1st Qu.:  7.60000   1st Qu.: 66.00  
    ##  Median : 12.30   Median : 10.40   Median : 14.70012   Median : 80.00  
    ##  Mean   : 13.95   Mean   : 11.51   Mean   : 18.17040   Mean   : 82.66  
    ##  3rd Qu.: 16.90   3rd Qu.: 14.10   3rd Qu.: 24.80000   3rd Qu.: 94.55  
    ##  Max.   :155.60   Max.   :128.30   Max.   :149.30012   Max.   :230.00  
    ##                                    NA's   :146         NA's   :146     
    ##    Weight_min    
    ##  Min.   : 34.60  
    ##  1st Qu.: 65.00  
    ##  Median : 77.70  
    ##  Mean   : 80.86  
    ##  3rd Qu.: 91.95  
    ##  Max.   :230.00  
    ##  NA's   :146
    head(icu_patients_df1)
    ##   RecordID Length_of_stay SAPS1 SOFA Survival in_hospital_death Days Status Age
    ## 1   132539              5     6    1       NA                 0 2408  FALSE  54
    ## 2   132540              8    16    8       NA                 0 2408  FALSE  76
    ## 3   132541             19    21   11       NA                 0 2408  FALSE  44
    ## 4   132543              9     7    1      575                 0  575   TRUE  68
    ## 5   132545              4    17    2      918                 0  918   TRUE  88
    ## 6   132547              6    14   11     1637                 0 1637   TRUE  64
    ##   Albumin_diff Albumin_max Albumin_min   ALP_diff ALP_max ALP_min  ALT_diff
    ## 1    0.2186633         3.2         3.1 118.147964     214     202  80.44617
    ## 2    0.8813367         2.1         2.2 252.147964     338     348  94.44617
    ## 3    0.6813367         2.7         2.3  31.147964     127     105  45.44617
    ## 4    1.4186633         4.4         4.4   9.147964     105     105 108.44617
    ## 5    0.3813367         2.7         2.6  56.852036      39      78  96.44617
    ## 6    0.4186633         3.4         3.3   5.147964     101     101  75.44617
    ##   ALT_max ALT_min  AST_diff AST_max AST_min Bilirubin_diff Bilirubin_max
    ## 1      40      75 131.35271      38      53       1.464039           0.4
    ## 2     206      26 116.35271      53      74       1.564039           1.2
    ## 3      91      75  65.64729     235     164       1.235961           3.0
    ## 4      12      12 154.35271      15      15       1.564039           0.2
    ## 5      24      32 154.35271      15      97       1.364039           0.4
    ## 6      60      45 122.35271     162      47       1.364039           0.4
    ##   Bilirubin_min  BUN_diff BUN_max BUN_min Cholesterol_diff Cholesterol_max
    ## 1           0.3 11.527053      13      13         16.42276             154
    ## 2           0.2  8.527053      18      16         28.42276             139
    ## 3           2.8 21.527053       8       3         56.42276             111
    ## 4           0.2  4.527053      23      20         37.42276             127
    ## 5           0.9 20.472947      45      45         55.42276             104
    ## 6           0.4  9.527053      19      15         55.57724             212
    ##   Cholesterol_min Creatinine_diff Creatinine_max Creatinine_min DiasABP_diff
    ## 1             140       0.4324463            0.8            0.8           NA
    ## 2             128       0.4324463            1.2            0.8     26.54421
    ## 3             100       0.9324463            0.4            0.3           NA
    ## 4             119       0.5324463            0.9            0.7           NA
    ## 5             101       0.2324463            1.0            1.0           NA
    ## 6             212       0.3324463            1.4            0.9     20.45579
    ##   DiasABP_max DiasABP_min  FiO2_diff FiO2_max FiO2_min GCS_diff GCS_max GCS_min
    ## 1          NA          NA 0.05192012      0.5      0.5 3.755971      15      15
    ## 2          81          32 0.44807988      1.0      0.4 8.244029      15       3
    ## 3          NA          NA 0.44807988      1.0      0.5 6.244029       8       5
    ## 4          NA          NA 0.44807988      1.0      0.4 3.755971      15      14
    ## 5          NA          NA 0.15192012      0.4      0.5 3.755971      15      15
    ## 6          79          55 0.05192012      0.5      0.5 4.244029       9       7
    ##   Gender Glucose_diff Glucose_max Glucose_min HCO3_diff HCO3_max HCO3_min
    ## 1 Female     65.14446         205         205  3.227452       26       26
    ## 2   Male     34.85554         105         105  1.772548       22       21
    ## 3 Female     20.85554         141         119  3.227452       26       24
    ## 4   Male     33.85554         129         106  5.227452       28       27
    ## 5 Female     26.85554         113         113  4.772548       18       18
    ## 6   Male    124.14446         264         197  3.772548       19       19
    ##    HCT_diff HCT_max HCT_min Height   HR_diff HR_max HR_min
    ## 1  2.739871    33.7    33.5     NA 29.077891     80     58
    ## 2  6.260129    29.7    24.7  175.3  7.077891     88     80
    ## 3  4.260129    28.5    26.7     NA 30.077891    113     57
    ## 4 10.339871    41.3    36.1  180.3 30.077891     88     57
    ## 5  8.360129    30.8    22.6     NA 20.077891     94     67
    ## 6 10.639871    41.6    36.8  180.3 16.077891     91     71
    ##                         ICUType    K_diff K_max K_min Lactate_diff Lactate_max
    ## 1                  Surgical ICU 0.2647934   4.4   4.4    0.9964037         1.9
    ## 2 Cardiac Surgery Recovery Unit 0.1647934   4.3   4.3    1.4964037         2.9
    ## 3                   Medical ICU 4.4647934   8.6   3.3    1.4964037         1.9
    ## 4                   Medical ICU 0.1352066   4.2   4.0    1.5964037         1.2
    ## 5                   Medical ICU 1.8647934   6.0   3.8    0.8964037         2.0
    ## 6            Coronary Care Unit 0.9647934   5.1   3.8    1.8964037         0.9
    ##   Lactate_min MAP_diff MAP_max MAP_min   Mg_diff Mg_max Mg_min   Na_diff Na_max
    ## 1         1.8 31.23164     109      56 0.4842982    1.5    1.5 2.2066071    137
    ## 2         1.3 34.76836     100      43 1.1157018    3.1    1.9 0.2066071    139
    ## 3         1.3 53.23164     131      71 0.6842982    1.9    1.3 2.2066071    140
    ## 4         1.5 24.23164     102      72 0.1157018    2.1    2.1 1.7933929    141
    ## 5         1.9  9.76836      78      68 0.4842982    1.5    1.5 0.7933929    140
    ## 6         1.3 24.23164     102      62 0.2842982    1.7    1.7 2.2066071    141
    ##   Na_min NIDiasABP_diff NIDiasABP_max NIDiasABP_min NIMAP_diff NIMAP_max
    ## 1    137       17.49101            65            40   17.04069     92.33
    ## 2    139       19.49101            65            38   26.38069     86.33
    ## 3    137       37.50899            95            66   34.28931    110.00
    ## 4    140       23.50899            81            54   24.98931    100.70
    ## 5    140       38.50899            96            29   29.98931    105.70
    ## 6    137       31.50899            89            52   26.58931    102.30
    ##   NIMAP_min NISysABP_diff NISysABP_max NISysABP_min PaCO2_diff PaCO2_max
    ## 1     58.67      40.30125          157           96   3.335797        37
    ## 2     49.33      44.69875          129           72   7.335797        41
    ## 3     83.33      33.30125          150          111   3.335797        37
    ## 4     73.00      23.30125          140          102   9.335797        38
    ## 5     63.67      39.30125          156          119   6.335797        34
    ## 6     61.67      35.69875          129           81   5.335797        45
    ##   PaCO2_min PaO2_diff PaO2_max PaO2_min    pH_diff pH_max pH_min Platelets_diff
    ## 1        38  47.61789      186      111 0.12011376   7.49   7.43       31.23069
    ## 2        33 286.38211      445       89 0.08011376   7.45   7.34       36.23069
    ## 3        37  93.61789       65       65 0.14011376   7.51   7.51      117.76931
    ## 4        31  94.61789      148       64 0.14011376   7.51   7.47      201.23069
    ## 5        35  80.61789       78       84 0.04011376   7.38   7.41       80.76931
    ## 6        35  80.61789      101       78 0.07988624   7.40   7.29       86.23069
    ##   Platelets_max Platelets_min RespRate_diff RespRate_max RespRate_min SaO2_diff
    ## 1           221           221       7.34858           24           12  3.246079
    ## 2           226           164      16.65142           36           11  1.753921
    ## 3            84            72      13.65142           33           18  2.246079
    ## 4           391           315       7.34858           21           12  1.753921
    ## 5           109           109       6.65142           26           15  3.246079
    ## 6           276           219      27.65142           47           20  1.246079
    ##   SaO2_max SaO2_min SysABP_diff SysABP_max SysABP_min Temp_diff Temp_max
    ## 1       98       94          NA         NA         NA  1.874083     38.1
    ## 2       99       97     50.3105        135         66  2.474083     37.9
    ## 3       95       95          NA         NA         NA  2.025917     39.0
    ## 4       99       97          NA         NA         NA  1.874083     36.7
    ## 5       97       94          NA         NA         NA  1.174083     37.8
    ## 6       97       96     43.3105        152         73  1.174083     37.8
    ##   Temp_min TroponinI_diff TroponinI_max TroponinI_min TroponinT_diff
    ## 1     35.1      5.1429448           1.0           0.3      0.4785006
    ## 2     34.5     26.2570552          31.7          16.1      0.6485006
    ## 3     36.7     31.2570552          33.4          36.7      0.8814994
    ## 4     35.1      0.8570552           5.9           6.3      0.6485006
    ## 5     35.8      0.1570552           5.6           5.6      0.6085006
    ## 6     35.8      4.1429448           1.3           1.3      0.6385006
    ##   TroponinT_max TroponinT_min Urine_diff Urine_max Urine_min   WBC_diff WBC_max
    ## 1          0.58          0.19  800.78242       900        30  0.9331524    11.2
    ## 2          0.43          0.02  670.78242       770         0  4.7331524    13.1
    ## 3          1.55          1.41  310.78242       410        30  8.4331524     4.2
    ## 4          0.10          0.02  600.78242       700       100  3.3331524    11.5
    ## 5          0.06          0.37   83.21758       150        16  8.3331524     3.8
    ## 6          0.03          0.10 1100.78242      1200        40 11.8668476    24.0
    ##   WBC_min Weight_diff Weight_max Weight_min
    ## 1    11.2          NA         NA         NA
    ## 2     7.4    4.699878       80.6       76.0
    ## 3     3.7   23.999878       56.7       56.7
    ## 4     8.8    3.900122       84.6       84.6
    ## 5     3.8          NA         NA         NA
    ## 6    14.4   33.300122      114.0      114.0
    1. Conduct basic exploratory data analysis on your variables of choice.
    library(ggplot2)
    library(gridExtra)
    
    #################################################################################
    ### CODE COPIED FROM TASK 2
    # create new variable PF ratio as part of our list of variables to include
    icu_patients_df1$PFratio<-icu_patients_df1$PaO2_min/icu_patients_df1$FiO2_max
    ### CODE COPIED FROM TASK 2
    #################################################################################
    
    summary(icu_patients_df1$Height) #max height is 426.7cm!? and min is 13.0cm - seems wrong
    ##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's 
    ##    13.0   162.6   170.2   170.0   177.8   426.7     992
    # Basic EDA for each variable
    
    table(icu_patients_df1$in_hospital_death) #297 deaths out of 2016 observations = 14.4%
    ## 
    ##    0    1 
    ## 1764  297
    # Write a function to plot box plots for each variable by in_hospital_death
    boxplot_eda <- function(variable){
      plot <- ggplot(data=icu_patients_df1, 
              mapping = aes(x = in_hospital_death=="1", 
                            y = icu_patients_df1[,variable])) + 
              geom_boxplot() +
              labs(title=paste('Box plot of',variable), 
                   x='In hospital death', y=variable)
      return(plot)
    }
    
    
    ### Continuous variables EDA and their interpretation ###
    
    #################################################################################
    ### CODE COPIED FROM TASK 2
    # continuous variables from the list of initial subset of explanatory variables
    cont_vars <- c('Age', 'Height', 'Weight_max', 'Albumin_min', 'Bilirubin_max',
                   'BUN_max', 'Creatinine_max', 'GCS_min', 'Glucose_min',
                   'Glucose_max', 'HCO3_min', 'HR_min', 'HR_max', 'K_min', 'K_max',
                   'Lactate_max', 'MAP_min', 'Na_min', 'Na_max', 'NISysABP_min',
                   'NISysABP_max', 'Platelets_min', 'PFratio', 'pH_min', 'pH_max',
                   'RespRate_min', 'RespRate_max', 'Temp_min', 'Temp_max',
                   'TroponinI_max', 'TroponinT_max', 'Urine_min', 'WBC_min', 'WBC_max')
    ### CODE COPIED FROM TASK 2
    #################################################################################
    
    # Loop through the continuous variables and produce box plots using the boxplot_eda() function 
    b <- list() # initialise an empty list to store the plots in
    for(i in 1:length(cont_vars)){
      b[[i]] <- boxplot_eda(cont_vars[i])
    }
    # arrange the list of plots in a 12 row grid using grid.arrange() from package{gridExtra}
    do.call(grid.arrange, c(b, nrow = 12))
    ## Warning: Removed 992 rows containing non-finite values (stat_boxplot).
    ## Warning: Removed 146 rows containing non-finite values (stat_boxplot).
    ## Warning: Removed 453 rows containing non-finite values (stat_boxplot).
    
    ## Warning: Removed 453 rows containing non-finite values (stat_boxplot).

    # Higher age in those that died
    # Some extreme illogical outliers in height variable
    # Similar weight median / IQR in both groups, but more high outliers in the alive group
    # Higher min albumin in those that died
    # Slightly higher max bilirubin in those that died
    # Higher max urea in those that died
    # Higher max creatinine in those that died
    # Lower GCS min in those that died
    # Similar min glucose in both groups
    # Slightly higher max glucose in those that died
    # Lower min HCO3 in those that died
    # Similar min HR in both groups
    # Slightly higher max HR in those that died
    # Similar min K in both groups
    # Similar max K in both groups
    # Slightly higher max lactate in those that died
    # Similar min MAP in both groups
    # Similar min Na in both groups
    # Similar max Na in both groups
    # Slightly lower min NISysABP in those that died
    # Similar max NISysABP in both groups
    # Similar min platelets in both groups
    # Similar PF ratio in both groups
    # Similar min pH in both groups - one extreme outlier
    # Similar pH max in both groups
    # Higher min RR in those that died
    # Higher max RR in those that died
    # Similar min temp in both groups
    # Similar max temp in both groups
    # Similar max troponinI in both groups
    # Similar max troponinT in both groups
    # Similar min urine in both groups
    # Slightly higher min WBC in those that died
    # Slightly higher max WBC in those that died
    ## had to split this chunk into two to allow making the big grid figure larger without affecting the others ##
    
    # Patients who died had higher SAPS1 and SOFA scores
    ggplot(data=icu_patients_df1, 
           mapping = aes(x = in_hospital_death=="1", y = SAPS1)) + geom_boxplot() +
           labs(title=paste('Box plot of SAPS1 scores'), 
                x='In hospital death', y='SAPS1 score')
    ## Warning: Removed 96 rows containing non-finite values (stat_boxplot).

    ggplot(data=icu_patients_df1, 
           mapping = aes(x = in_hospital_death=="1", y = SOFA)) + geom_boxplot() +
           labs(title=paste('Box plot of SOFA scores'), 
                x='In hospital death', y='SOFA score')

    ### Categorical variables EDA and their interpretation ###
    
    # cardiac surgery recovery unit have a smaller death circle compared to the other 3 ICU units
    # ie less proportion of in hospital deaths compared to alive
    icutype_plot <- ggplot(data=icu_patients_df1, 
                           mapping = aes(x = in_hospital_death=="1", y = ICUType)) + 
                    geom_count(aes(size = after_stat(prop), group = ICUType)) + 
                    scale_size_area(max_size = 10) + 
                    labs(title=paste('Proportion of patients by ICU type'), 
                         x='In hospital death', size='Proportion of patients')
    
    # difficult to say, roughly same amount of men/women died as a proportion of the alive group
    gender_plot <- ggplot(data=icu_patients_df1, 
                          mapping = aes(x = in_hospital_death=="1", y = Gender)) + 
                   geom_count(aes(size = after_stat(prop), group = ICUType)) + 
                   scale_size_area(max_size = 20) + 
                    labs(title=paste('Proportion of patients by gender'), 
                         x='In hospital death', size='Proportion of patients')
    
    # arrange the categorical variable plots side-by-side
    grid.arrange(icutype_plot, gender_plot, nrow=1)

    1. Fit appropriate univariate logistic regression models.
    # univariate comparisons above
    # removed: Mg_min, Na_min, Na_max, MAP_diff, MAP_max
    # now in order as per above list
    
    
    age_glm <- glm(in_hospital_death ~ Age, data=icu_patients_df1, family="binomial")
    summary(age_glm) # is significant
    ## 
    ## Call:
    ## glm(formula = in_hospital_death ~ Age, family = "binomial", data = icu_patients_df1)
    ## 
    ## Deviance Residuals: 
    ##     Min       1Q   Median       3Q      Max  
    ## -0.7522  -0.6264  -0.5111  -0.3919   2.5135  
    ## 
    ## Coefficients:
    ##              Estimate Std. Error z value Pr(>|z|)    
    ## (Intercept) -3.761624   0.303337 -12.401  < 2e-16 ***
    ## Age          0.029376   0.004229   6.947 3.73e-12 ***
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ## 
    ## (Dispersion parameter for binomial family taken to be 1)
    ## 
    ##     Null deviance: 1699.7  on 2060  degrees of freedom
    ## Residual deviance: 1644.9  on 2059  degrees of freedom
    ## AIC: 1648.9
    ## 
    ## Number of Fisher Scoring iterations: 5
    gender_glm <- glm(in_hospital_death ~ Gender, data=icu_patients_df1, family="binomial")
    summary(gender_glm) # NOT significant
    ## 
    ## Call:
    ## glm(formula = in_hospital_death ~ Gender, family = "binomial", 
    ##     data = icu_patients_df1)
    ## 
    ## Deviance Residuals: 
    ##     Min       1Q   Median       3Q      Max  
    ## -0.5612  -0.5612  -0.5553  -0.5553   1.9728  
    ## 
    ## Coefficients:
    ##             Estimate Std. Error z value Pr(>|z|)    
    ## (Intercept) -1.76894    0.09381 -18.856   <2e-16 ***
    ## GenderMale  -0.02281    0.12615  -0.181    0.856    
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ## 
    ## (Dispersion parameter for binomial family taken to be 1)
    ## 
    ##     Null deviance: 1699.7  on 2060  degrees of freedom
    ## Residual deviance: 1699.7  on 2059  degrees of freedom
    ## AIC: 1703.7
    ## 
    ## Number of Fisher Scoring iterations: 4
    icuType_glm <- glm(in_hospital_death ~ ICUType, data=icu_patients_df1, family="binomial")
    summary(icuType_glm) # cardiac surgery recovery unit is significant
    ## 
    ## Call:
    ## glm(formula = in_hospital_death ~ ICUType, family = "binomial", 
    ##     data = icu_patients_df1)
    ## 
    ## Deviance Residuals: 
    ##     Min       1Q   Median       3Q      Max  
    ## -0.6402  -0.6402  -0.5615  -0.3458   2.3861  
    ## 
    ## Coefficients:
    ##                                      Estimate Std. Error z value Pr(>|z|)    
    ## (Intercept)                           -1.6463     0.1576 -10.443  < 2e-16 ***
    ## ICUTypeCardiac Surgery Recovery Unit  -1.1407     0.2563  -4.451 8.55e-06 ***
    ## ICUTypeMedical ICU                     0.1653     0.1824   0.906    0.365    
    ## ICUTypeSurgical ICU                   -0.1214     0.2001  -0.607    0.544    
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ## 
    ## (Dispersion parameter for binomial family taken to be 1)
    ## 
    ##     Null deviance: 1699.7  on 2060  degrees of freedom
    ## Residual deviance: 1655.3  on 2057  degrees of freedom
    ## AIC: 1663.3
    ## 
    ## Number of Fisher Scoring iterations: 5
    # height variable not used
    
    maxWeight_glm <- glm(in_hospital_death ~ Weight_max, data=icu_patients_df1, family="binomial")
    summary(maxWeight_glm) # is significant
    ## 
    ## Call:
    ## glm(formula = in_hospital_death ~ Weight_max, family = "binomial", 
    ##     data = icu_patients_df1)
    ## 
    ## Deviance Residuals: 
    ##     Min       1Q   Median       3Q      Max  
    ## -0.6460  -0.5846  -0.5605  -0.5231   2.1768  
    ## 
    ## Coefficients:
    ##              Estimate Std. Error z value Pr(>|z|)    
    ## (Intercept) -1.246092   0.242568  -5.137 2.79e-07 ***
    ## Weight_max  -0.006212   0.002912  -2.133   0.0329 *  
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ## 
    ## (Dispersion parameter for binomial family taken to be 1)
    ## 
    ##     Null deviance: 1604.2  on 1914  degrees of freedom
    ## Residual deviance: 1599.4  on 1913  degrees of freedom
    ##   (146 observations deleted due to missingness)
    ## AIC: 1603.4
    ## 
    ## Number of Fisher Scoring iterations: 4
    minAlbumin_glm <- glm(in_hospital_death ~ Albumin_min, data=icu_patients_df1, family="binomial")
    summary(minAlbumin_glm) # is significant
    ## 
    ## Call:
    ## glm(formula = in_hospital_death ~ Albumin_min, family = "binomial", 
    ##     data = icu_patients_df1)
    ## 
    ## Deviance Residuals: 
    ##     Min       1Q   Median       3Q      Max  
    ## -0.7948  -0.5887  -0.5385  -0.4595   2.2842  
    ## 
    ## Coefficients:
    ##             Estimate Std. Error z value Pr(>|z|)    
    ## (Intercept) -0.36392    0.29389  -1.238    0.216    
    ## Albumin_min -0.48186    0.09987  -4.825  1.4e-06 ***
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ## 
    ## (Dispersion parameter for binomial family taken to be 1)
    ## 
    ##     Null deviance: 1699.7  on 2060  degrees of freedom
    ## Residual deviance: 1676.0  on 2059  degrees of freedom
    ## AIC: 1680
    ## 
    ## Number of Fisher Scoring iterations: 4
    maxBili_glm <- glm(in_hospital_death ~ Bilirubin_max, data=icu_patients_df1, family="binomial")
    summary(maxBili_glm) # is significant
    ## 
    ## Call:
    ## glm(formula = in_hospital_death ~ Bilirubin_max, family = "binomial", 
    ##     data = icu_patients_df1)
    ## 
    ## Deviance Residuals: 
    ##     Min       1Q   Median       3Q      Max  
    ## -1.3889  -0.5421  -0.5363  -0.5321   2.0174  
    ## 
    ## Coefficients:
    ##               Estimate Std. Error z value Pr(>|z|)    
    ## (Intercept)   -1.90053    0.06866 -27.679  < 2e-16 ***
    ## Bilirubin_max  0.05692    0.01135   5.013 5.35e-07 ***
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ## 
    ## (Dispersion parameter for binomial family taken to be 1)
    ## 
    ##     Null deviance: 1699.7  on 2060  degrees of freedom
    ## Residual deviance: 1676.8  on 2059  degrees of freedom
    ## AIC: 1680.8
    ## 
    ## Number of Fisher Scoring iterations: 4
    maxUrea_glm <- glm(in_hospital_death ~ BUN_max, data=icu_patients_df1, family="binomial")
    summary(maxUrea_glm) # is significant
    ## 
    ## Call:
    ## glm(formula = in_hospital_death ~ BUN_max, family = "binomial", 
    ##     data = icu_patients_df1)
    ## 
    ## Deviance Residuals: 
    ##     Min       1Q   Median       3Q      Max  
    ## -2.0462  -0.5269  -0.4789  -0.4443   2.2309  
    ## 
    ## Coefficients:
    ##              Estimate Std. Error z value Pr(>|z|)    
    ## (Intercept) -2.492189   0.103693 -24.034   <2e-16 ***
    ## BUN_max      0.022610   0.002347   9.634   <2e-16 ***
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ## 
    ## (Dispersion parameter for binomial family taken to be 1)
    ## 
    ##     Null deviance: 1699.7  on 2060  degrees of freedom
    ## Residual deviance: 1607.3  on 2059  degrees of freedom
    ## AIC: 1611.3
    ## 
    ## Number of Fisher Scoring iterations: 4
    maxCr_glm <- glm(in_hospital_death ~ Creatinine_max, data=icu_patients_df1, family="binomial")
    summary(maxCr_glm) # is significant
    ## 
    ## Call:
    ## glm(formula = in_hospital_death ~ Creatinine_max, family = "binomial", 
    ##     data = icu_patients_df1)
    ## 
    ## Deviance Residuals: 
    ##     Min       1Q   Median       3Q      Max  
    ## -1.8627  -0.5433  -0.5270  -0.5151   2.0633  
    ## 
    ## Coefficients:
    ##                Estimate Std. Error z value Pr(>|z|)    
    ## (Intercept)    -2.05087    0.08430 -24.328  < 2e-16 ***
    ## Creatinine_max  0.16325    0.03135   5.208 1.91e-07 ***
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ## 
    ## (Dispersion parameter for binomial family taken to be 1)
    ## 
    ##     Null deviance: 1699.7  on 2060  degrees of freedom
    ## Residual deviance: 1674.4  on 2059  degrees of freedom
    ## AIC: 1678.4
    ## 
    ## Number of Fisher Scoring iterations: 4
    minGCS_glm <- glm(in_hospital_death ~ GCS_min, data=icu_patients_df1, family="binomial")
    summary(minGCS_glm) # is significant
    ## 
    ## Call:
    ## glm(formula = in_hospital_death ~ GCS_min, family = "binomial", 
    ##     data = icu_patients_df1)
    ## 
    ## Deviance Residuals: 
    ##     Min       1Q   Median       3Q      Max  
    ## -0.6238  -0.6238  -0.5394  -0.4853   2.0964  
    ## 
    ## Coefficients:
    ##             Estimate Std. Error z value Pr(>|z|)    
    ## (Intercept) -1.40261    0.12298 -11.405  < 2e-16 ***
    ## GCS_min     -0.04514    0.01317  -3.426 0.000612 ***
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ## 
    ## (Dispersion parameter for binomial family taken to be 1)
    ## 
    ##     Null deviance: 1699.7  on 2060  degrees of freedom
    ## Residual deviance: 1687.7  on 2059  degrees of freedom
    ## AIC: 1691.7
    ## 
    ## Number of Fisher Scoring iterations: 4
    minGlu_glm <- glm(in_hospital_death ~ Glucose_min, data=icu_patients_df1, family="binomial")
    summary(minGlu_glm) # NOT significant
    ## 
    ## Call:
    ## glm(formula = in_hospital_death ~ Glucose_min, family = "binomial", 
    ##     data = icu_patients_df1)
    ## 
    ## Deviance Residuals: 
    ##     Min       1Q   Median       3Q      Max  
    ## -0.7799  -0.5613  -0.5522  -0.5428   2.0271  
    ## 
    ## Coefficients:
    ##              Estimate Std. Error z value Pr(>|z|)    
    ## (Intercept) -1.967537   0.171241 -11.490   <2e-16 ***
    ## Glucose_min  0.001476   0.001253   1.178    0.239    
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ## 
    ## (Dispersion parameter for binomial family taken to be 1)
    ## 
    ##     Null deviance: 1699.7  on 2060  degrees of freedom
    ## Residual deviance: 1698.4  on 2059  degrees of freedom
    ## AIC: 1702.4
    ## 
    ## Number of Fisher Scoring iterations: 4
    maxGlu_glm <- glm(in_hospital_death ~ Glucose_max, data=icu_patients_df1, family="binomial")
    summary(maxGlu_glm) # is significant
    ## 
    ## Call:
    ## glm(formula = in_hospital_death ~ Glucose_max, family = "binomial", 
    ##     data = icu_patients_df1)
    ## 
    ## Deviance Residuals: 
    ##     Min       1Q   Median       3Q      Max  
    ## -1.4117  -0.5572  -0.5343  -0.5162   2.0872  
    ## 
    ## Coefficients:
    ##               Estimate Std. Error z value Pr(>|z|)    
    ## (Intercept) -2.1865370  0.1202802 -18.179  < 2e-16 ***
    ## Glucose_max  0.0023817  0.0005819   4.093 4.25e-05 ***
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ## 
    ## (Dispersion parameter for binomial family taken to be 1)
    ## 
    ##     Null deviance: 1699.7  on 2060  degrees of freedom
    ## Residual deviance: 1684.2  on 2059  degrees of freedom
    ## AIC: 1688.2
    ## 
    ## Number of Fisher Scoring iterations: 4
    minHCO3_glm <- glm(in_hospital_death ~ HCO3_min, data=icu_patients_df1, family="binomial")
    summary(minHCO3_glm) # is significant
    ## 
    ## Call:
    ## glm(formula = in_hospital_death ~ HCO3_min, family = "binomial", 
    ##     data = icu_patients_df1)
    ## 
    ## Deviance Residuals: 
    ##     Min       1Q   Median       3Q      Max  
    ## -0.9781  -0.5748  -0.5165  -0.4634   2.6504  
    ## 
    ## Coefficients:
    ##             Estimate Std. Error z value Pr(>|z|)    
    ## (Intercept) -0.10497    0.29323  -0.358     0.72    
    ## HCO3_min    -0.07675    0.01345  -5.705 1.17e-08 ***
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ## 
    ## (Dispersion parameter for binomial family taken to be 1)
    ## 
    ##     Null deviance: 1699.7  on 2060  degrees of freedom
    ## Residual deviance: 1666.8  on 2059  degrees of freedom
    ## AIC: 1670.8
    ## 
    ## Number of Fisher Scoring iterations: 4
    minHR_glm <- glm(in_hospital_death ~ HR_min, data=icu_patients_df1, family="binomial")
    summary(minHR_glm) # NOT significant
    ## 
    ## Call:
    ## glm(formula = in_hospital_death ~ HR_min, family = "binomial", 
    ##     data = icu_patients_df1)
    ## 
    ## Deviance Residuals: 
    ##     Min       1Q   Median       3Q      Max  
    ## -0.6235  -0.5656  -0.5528  -0.5390   2.1087  
    ## 
    ## Coefficients:
    ##              Estimate Std. Error z value Pr(>|z|)    
    ## (Intercept) -2.108733   0.301434  -6.996 2.64e-12 ***
    ## HR_min       0.004520   0.004052   1.115    0.265    
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ## 
    ## (Dispersion parameter for binomial family taken to be 1)
    ## 
    ##     Null deviance: 1699.7  on 2060  degrees of freedom
    ## Residual deviance: 1698.4  on 2059  degrees of freedom
    ## AIC: 1702.4
    ## 
    ## Number of Fisher Scoring iterations: 4
    maxHR_glm <- glm(in_hospital_death ~ HR_max, data=icu_patients_df1, family="binomial")
    summary(maxHR_glm) # is significant
    ## 
    ## Call:
    ## glm(formula = in_hospital_death ~ HR_max, family = "binomial", 
    ##     data = icu_patients_df1)
    ## 
    ## Deviance Residuals: 
    ##     Min       1Q   Median       3Q      Max  
    ## -1.1194  -0.5733  -0.5402  -0.5067   2.1517  
    ## 
    ## Coefficients:
    ##              Estimate Std. Error z value Pr(>|z|)    
    ## (Intercept) -2.707555   0.303251  -8.928  < 2e-16 ***
    ## HR_max       0.008565   0.002707   3.164  0.00156 ** 
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ## 
    ## (Dispersion parameter for binomial family taken to be 1)
    ## 
    ##     Null deviance: 1699.7  on 2060  degrees of freedom
    ## Residual deviance: 1689.9  on 2059  degrees of freedom
    ## AIC: 1693.9
    ## 
    ## Number of Fisher Scoring iterations: 4
    minK_glm <- glm(in_hospital_death ~ K_min, data=icu_patients_df1, family="binomial")
    summary(minK_glm) # NOT significant
    ## 
    ## Call:
    ## glm(formula = in_hospital_death ~ K_min, family = "binomial", 
    ##     data = icu_patients_df1)
    ## 
    ## Deviance Residuals: 
    ##     Min       1Q   Median       3Q      Max  
    ## -0.6024  -0.5647  -0.5546  -0.5447   2.0345  
    ## 
    ## Coefficients:
    ##             Estimate Std. Error z value Pr(>|z|)    
    ## (Intercept) -1.47413    0.42361  -3.480 0.000502 ***
    ## K_min       -0.07804    0.10660  -0.732 0.464083    
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ## 
    ## (Dispersion parameter for binomial family taken to be 1)
    ## 
    ##     Null deviance: 1699.7  on 2060  degrees of freedom
    ## Residual deviance: 1699.1  on 2059  degrees of freedom
    ## AIC: 1703.1
    ## 
    ## Number of Fisher Scoring iterations: 4
    maxK_glm <- glm(in_hospital_death ~ K_max, data=icu_patients_df1, family="binomial")
    summary(maxK_glm) # NOT significant
    ## 
    ## Call:
    ## glm(formula = in_hospital_death ~ K_max, family = "binomial", 
    ##     data = icu_patients_df1)
    ## 
    ## Deviance Residuals: 
    ##     Min       1Q   Median       3Q      Max  
    ## -1.2402  -0.5620  -0.5512  -0.5380   2.0561  
    ## 
    ## Coefficients:
    ##             Estimate Std. Error z value Pr(>|z|)    
    ## (Intercept) -2.24634    0.28233  -7.956 1.77e-15 ***
    ## K_max        0.10449    0.06153   1.698   0.0895 .  
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ## 
    ## (Dispersion parameter for binomial family taken to be 1)
    ## 
    ##     Null deviance: 1699.7  on 2060  degrees of freedom
    ## Residual deviance: 1697.0  on 2059  degrees of freedom
    ## AIC: 1701
    ## 
    ## Number of Fisher Scoring iterations: 4
    maxLactate_glm <- glm(in_hospital_death ~ Lactate_max, data=icu_patients_df1, family="binomial")
    summary(maxLactate_glm) # is significant
    ## 
    ## Call:
    ## glm(formula = in_hospital_death ~ Lactate_max, family = "binomial", 
    ##     data = icu_patients_df1)
    ## 
    ## Deviance Residuals: 
    ##     Min       1Q   Median       3Q      Max  
    ## -1.1726  -0.5544  -0.5200  -0.4939   2.1212  
    ## 
    ## Coefficients:
    ##             Estimate Std. Error z value Pr(>|z|)    
    ## (Intercept)  -2.1932     0.1005 -21.820  < 2e-16 ***
    ## Lactate_max   0.1372     0.0244   5.625 1.86e-08 ***
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ## 
    ## (Dispersion parameter for binomial family taken to be 1)
    ## 
    ##     Null deviance: 1699.7  on 2060  degrees of freedom
    ## Residual deviance: 1669.5  on 2059  degrees of freedom
    ## AIC: 1673.5
    ## 
    ## Number of Fisher Scoring iterations: 4
    minMAP_glm <- glm(in_hospital_death ~ MAP_min, data=icu_patients_df1, family="binomial")
    summary(minMAP_glm) # NOT significant
    ## 
    ## Call:
    ## glm(formula = in_hospital_death ~ MAP_min, family = "binomial", 
    ##     data = icu_patients_df1)
    ## 
    ## Deviance Residuals: 
    ##     Min       1Q   Median       3Q      Max  
    ## -0.6583  -0.5674  -0.5551  -0.5341   2.4214  
    ## 
    ## Coefficients:
    ##              Estimate Std. Error z value Pr(>|z|)    
    ## (Intercept) -1.413112   0.257434  -5.489 4.04e-08 ***
    ## MAP_min     -0.005926   0.004051  -1.463    0.143    
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ## 
    ## (Dispersion parameter for binomial family taken to be 1)
    ## 
    ##     Null deviance: 1699.7  on 2060  degrees of freedom
    ## Residual deviance: 1697.4  on 2059  degrees of freedom
    ## AIC: 1701.4
    ## 
    ## Number of Fisher Scoring iterations: 4
    minNa_glm <- glm(in_hospital_death ~ Na_min, data=icu_patients_df1, family="binomial")
    summary(minNa_glm) # is significant
    ## 
    ## Call:
    ## glm(formula = in_hospital_death ~ Na_min, family = "binomial", 
    ##     data = icu_patients_df1)
    ## 
    ## Deviance Residuals: 
    ##     Min       1Q   Median       3Q      Max  
    ## -0.9061  -0.5706  -0.5490  -0.5282   2.2298  
    ## 
    ## Coefficients:
    ##             Estimate Std. Error z value Pr(>|z|)  
    ## (Intercept)  2.04227    1.79129   1.140   0.2542  
    ## Na_min      -0.02776    0.01301  -2.133   0.0329 *
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ## 
    ## (Dispersion parameter for binomial family taken to be 1)
    ## 
    ##     Null deviance: 1699.7  on 2060  degrees of freedom
    ## Residual deviance: 1695.3  on 2059  degrees of freedom
    ## AIC: 1699.3
    ## 
    ## Number of Fisher Scoring iterations: 4
    maxNa_glm <- glm(in_hospital_death ~ Na_max, data=icu_patients_df1, family="binomial")
    summary(maxNa_glm) # NOT significant
    ## 
    ## Call:
    ## glm(formula = in_hospital_death ~ Na_max, family = "binomial", 
    ##     data = icu_patients_df1)
    ## 
    ## Deviance Residuals: 
    ##     Min       1Q   Median       3Q      Max  
    ## -0.6176  -0.5615  -0.5573  -0.5491   2.0760  
    ## 
    ## Coefficients:
    ##              Estimate Std. Error z value Pr(>|z|)
    ## (Intercept) -0.664686   1.927556  -0.345    0.730
    ## Na_max      -0.007993   0.013793  -0.580    0.562
    ## 
    ## (Dispersion parameter for binomial family taken to be 1)
    ## 
    ##     Null deviance: 1699.7  on 2060  degrees of freedom
    ## Residual deviance: 1699.4  on 2059  degrees of freedom
    ## AIC: 1703.4
    ## 
    ## Number of Fisher Scoring iterations: 4
    minNISys_ABP_glm <- glm(in_hospital_death ~ NISysABP_min, data=icu_patients_df1, family="binomial")
    summary(minNISys_ABP_glm) # is significant
    ## 
    ## Call:
    ## glm(formula = in_hospital_death ~ NISysABP_min, family = "binomial", 
    ##     data = icu_patients_df1)
    ## 
    ## Deviance Residuals: 
    ##     Min       1Q   Median       3Q      Max  
    ## -0.9728  -0.6135  -0.5731  -0.5005   2.3871  
    ## 
    ## Coefficients:
    ##               Estimate Std. Error z value Pr(>|z|)    
    ## (Intercept)  -0.450605   0.328983  -1.370 0.170783    
    ## NISysABP_min -0.012922   0.003466  -3.728 0.000193 ***
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ## 
    ## (Dispersion parameter for binomial family taken to be 1)
    ## 
    ##     Null deviance: 1403.1  on 1607  degrees of freedom
    ## Residual deviance: 1388.5  on 1606  degrees of freedom
    ##   (453 observations deleted due to missingness)
    ## AIC: 1392.5
    ## 
    ## Number of Fisher Scoring iterations: 4
    maxNISys_ABP_glm <- glm(in_hospital_death ~ NISysABP_max, data=icu_patients_df1, family="binomial")
    summary(maxNISys_ABP_glm) # NOT significant
    ## 
    ## Call:
    ## glm(formula = in_hospital_death ~ NISysABP_max, family = "binomial", 
    ##     data = icu_patients_df1)
    ## 
    ## Deviance Residuals: 
    ##     Min       1Q   Median       3Q      Max  
    ## -0.6098  -0.5886  -0.5846  -0.5799   1.9414  
    ## 
    ## Coefficients:
    ##                Estimate Std. Error z value Pr(>|z|)    
    ## (Intercept)  -1.7826689  0.3544507  -5.029 4.92e-07 ***
    ## NISysABP_max  0.0007759  0.0024679   0.314    0.753    
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ## 
    ## (Dispersion parameter for binomial family taken to be 1)
    ## 
    ##     Null deviance: 1403.1  on 1607  degrees of freedom
    ## Residual deviance: 1403.0  on 1606  degrees of freedom
    ##   (453 observations deleted due to missingness)
    ## AIC: 1407
    ## 
    ## Number of Fisher Scoring iterations: 3
    minPlt_glm <- glm(in_hospital_death ~ Platelets_min, data=icu_patients_df1, family="binomial")
    summary(minPlt_glm) # NOT significant
    ## 
    ## Call:
    ## glm(formula = in_hospital_death ~ Platelets_min, family = "binomial", 
    ##     data = icu_patients_df1)
    ## 
    ## Deviance Residuals: 
    ##     Min       1Q   Median       3Q      Max  
    ## -0.6122  -0.5735  -0.5558  -0.5260   2.2141  
    ## 
    ## Coefficients:
    ##                 Estimate Std. Error z value Pr(>|z|)    
    ## (Intercept)   -1.5693181  0.1352494 -11.603   <2e-16 ***
    ## Platelets_min -0.0010963  0.0006322  -1.734   0.0829 .  
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ## 
    ## (Dispersion parameter for binomial family taken to be 1)
    ## 
    ##     Null deviance: 1699.7  on 2060  degrees of freedom
    ## Residual deviance: 1696.6  on 2059  degrees of freedom
    ## AIC: 1700.6
    ## 
    ## Number of Fisher Scoring iterations: 4
    maxPFratio_glm <- glm(in_hospital_death ~ PFratio, data=icu_patients_df1, family="binomial")
    summary(maxPFratio_glm) # NOT significant
    ## 
    ## Call:
    ## glm(formula = in_hospital_death ~ PFratio, family = "binomial", 
    ##     data = icu_patients_df1)
    ## 
    ## Deviance Residuals: 
    ##     Min       1Q   Median       3Q      Max  
    ## -0.5806  -0.5687  -0.5595  -0.5398   2.1022  
    ## 
    ## Coefficients:
    ##               Estimate Std. Error z value Pr(>|z|)    
    ## (Intercept) -1.6790207  0.1148206 -14.623   <2e-16 ***
    ## PFratio     -0.0006772  0.0006452  -1.049    0.294    
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ## 
    ## (Dispersion parameter for binomial family taken to be 1)
    ## 
    ##     Null deviance: 1699.7  on 2060  degrees of freedom
    ## Residual deviance: 1698.5  on 2059  degrees of freedom
    ## AIC: 1702.5
    ## 
    ## Number of Fisher Scoring iterations: 4
    minpH_glm <- glm(in_hospital_death ~ pH_min, data=icu_patients_df1, family="binomial")
    summary(minpH_glm) # is significant
    ## 
    ## Call:
    ## glm(formula = in_hospital_death ~ pH_min, family = "binomial", 
    ##     data = icu_patients_df1)
    ## 
    ## Deviance Residuals: 
    ##     Min       1Q   Median       3Q      Max  
    ## -0.9980  -0.5733  -0.5358  -0.4868   2.2874  
    ## 
    ## Coefficients:
    ##             Estimate Std. Error z value Pr(>|z|)    
    ## (Intercept)  19.5912     4.8996   3.998 6.37e-05 ***
    ## pH_min       -2.9197     0.6699  -4.358 1.31e-05 ***
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ## 
    ## (Dispersion parameter for binomial family taken to be 1)
    ## 
    ##     Null deviance: 1699.7  on 2060  degrees of freedom
    ## Residual deviance: 1677.4  on 2059  degrees of freedom
    ## AIC: 1681.4
    ## 
    ## Number of Fisher Scoring iterations: 4
    maxpH_glm <- glm(in_hospital_death ~ pH_max, data=icu_patients_df1, family="binomial")
    summary(maxpH_glm) # NOT significant
    ## 
    ## Call:
    ## glm(formula = in_hospital_death ~ pH_max, family = "binomial", 
    ##     data = icu_patients_df1)
    ## 
    ## Deviance Residuals: 
    ##     Min       1Q   Median       3Q      Max  
    ## -0.6684  -0.5677  -0.5523  -0.5297   2.0743  
    ## 
    ## Coefficients:
    ##             Estimate Std. Error z value Pr(>|z|)
    ## (Intercept)   9.3001     7.0197   1.325    0.185
    ## pH_max       -1.4944     0.9469  -1.578    0.115
    ## 
    ## (Dispersion parameter for binomial family taken to be 1)
    ## 
    ##     Null deviance: 1699.7  on 2060  degrees of freedom
    ## Residual deviance: 1697.2  on 2059  degrees of freedom
    ## AIC: 1701.2
    ## 
    ## Number of Fisher Scoring iterations: 4
    minRR_glm <- glm(in_hospital_death ~ RespRate_min, data=icu_patients_df1, family="binomial")
    summary(minRR_glm) # is significant
    ## 
    ## Call:
    ## glm(formula = in_hospital_death ~ RespRate_min, family = "binomial", 
    ##     data = icu_patients_df1)
    ## 
    ## Deviance Residuals: 
    ##     Min       1Q   Median       3Q      Max  
    ## -0.7929  -0.5872  -0.5222  -0.4636   2.3445  
    ## 
    ## Coefficients:
    ##              Estimate Std. Error z value Pr(>|z|)    
    ## (Intercept)  -3.01958    0.25802 -11.703  < 2e-16 ***
    ## RespRate_min  0.08432    0.01656   5.091 3.57e-07 ***
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ## 
    ## (Dispersion parameter for binomial family taken to be 1)
    ## 
    ##     Null deviance: 1699.7  on 2060  degrees of freedom
    ## Residual deviance: 1673.6  on 2059  degrees of freedom
    ## AIC: 1677.6
    ## 
    ## Number of Fisher Scoring iterations: 4
    maxRR_glm <- glm(in_hospital_death ~ RespRate_max, data=icu_patients_df1, family="binomial")
    summary(maxRR_glm) # is significant
    ## 
    ## Call:
    ## glm(formula = in_hospital_death ~ RespRate_max, family = "binomial", 
    ##     data = icu_patients_df1)
    ## 
    ## Deviance Residuals: 
    ##     Min       1Q   Median       3Q      Max  
    ## -1.4489  -0.5679  -0.5233  -0.4817   2.1771  
    ## 
    ## Coefficients:
    ##               Estimate Std. Error z value Pr(>|z|)    
    ## (Intercept)  -2.835656   0.235885 -12.021  < 2e-16 ***
    ## RespRate_max  0.035250   0.007412   4.756 1.98e-06 ***
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ## 
    ## (Dispersion parameter for binomial family taken to be 1)
    ## 
    ##     Null deviance: 1699.7  on 2060  degrees of freedom
    ## Residual deviance: 1677.8  on 2059  degrees of freedom
    ## AIC: 1681.8
    ## 
    ## Number of Fisher Scoring iterations: 4
    minTemp_glm <- glm(in_hospital_death ~ Temp_min, data=icu_patients_df1, family="binomial")
    summary(minTemp_glm) # is significant
    ## 
    ## Call:
    ## glm(formula = in_hospital_death ~ Temp_min, family = "binomial", 
    ##     data = icu_patients_df1)
    ## 
    ## Deviance Residuals: 
    ##     Min       1Q   Median       3Q      Max  
    ## -0.8918  -0.5741  -0.5409  -0.4973   2.2040  
    ## 
    ## Coefficients:
    ##             Estimate Std. Error z value Pr(>|z|)    
    ## (Intercept)   7.4599     2.3473   3.178  0.00148 ** 
    ## Temp_min     -0.2571     0.0654  -3.931 8.45e-05 ***
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ## 
    ## (Dispersion parameter for binomial family taken to be 1)
    ## 
    ##     Null deviance: 1699.7  on 2060  degrees of freedom
    ## Residual deviance: 1684.3  on 2059  degrees of freedom
    ## AIC: 1688.3
    ## 
    ## Number of Fisher Scoring iterations: 4
    maxTemp_glm <- glm(in_hospital_death ~ Temp_max, data=icu_patients_df1, family="binomial")
    summary(maxTemp_glm) # NOT significant
    ## 
    ## Call:
    ## glm(formula = in_hospital_death ~ Temp_max, family = "binomial", 
    ##     data = icu_patients_df1)
    ## 
    ## Deviance Residuals: 
    ##     Min       1Q   Median       3Q      Max  
    ## -0.6077  -0.5689  -0.5549  -0.5366   2.1386  
    ## 
    ## Coefficients:
    ##             Estimate Std. Error z value Pr(>|z|)
    ## (Intercept)  1.60419    3.08152   0.521    0.603
    ## Temp_max    -0.08988    0.08183  -1.098    0.272
    ## 
    ## (Dispersion parameter for binomial family taken to be 1)
    ## 
    ##     Null deviance: 1699.7  on 2060  degrees of freedom
    ## Residual deviance: 1698.5  on 2059  degrees of freedom
    ## AIC: 1702.5
    ## 
    ## Number of Fisher Scoring iterations: 4
    maxTropI_glm <- glm(in_hospital_death ~ TroponinI_max, data=icu_patients_df1, family="binomial")
    summary(maxTropI_glm) # NOT significant
    ## 
    ## Call:
    ## glm(formula = in_hospital_death ~ TroponinI_max, family = "binomial", 
    ##     data = icu_patients_df1)
    ## 
    ## Deviance Residuals: 
    ##     Min       1Q   Median       3Q      Max  
    ## -0.5736  -0.5688  -0.5565  -0.5350   2.0415  
    ## 
    ## Coefficients:
    ##                Estimate Std. Error z value Pr(>|z|)    
    ## (Intercept)   -1.719798   0.090789 -18.943   <2e-16 ***
    ## TroponinI_max -0.005329   0.005774  -0.923    0.356    
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ## 
    ## (Dispersion parameter for binomial family taken to be 1)
    ## 
    ##     Null deviance: 1699.7  on 2060  degrees of freedom
    ## Residual deviance: 1698.8  on 2059  degrees of freedom
    ## AIC: 1702.8
    ## 
    ## Number of Fisher Scoring iterations: 4
    maxTropT_glm <- glm(in_hospital_death ~ TroponinT_max, data=icu_patients_df1, family="binomial")
    summary(maxTropT_glm) # is significant
    ## 
    ## Call:
    ## glm(formula = in_hospital_death ~ TroponinT_max, family = "binomial", 
    ##     data = icu_patients_df1)
    ## 
    ## Deviance Residuals: 
    ##     Min       1Q   Median       3Q      Max  
    ## -1.0740  -0.5503  -0.5430  -0.5416   1.9965  
    ## 
    ## Coefficients:
    ##               Estimate Std. Error z value Pr(>|z|)    
    ## (Intercept)   -1.84719    0.06917 -26.705   <2e-16 ***
    ## TroponinT_max  0.06537    0.02638   2.478   0.0132 *  
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ## 
    ## (Dispersion parameter for binomial family taken to be 1)
    ## 
    ##     Null deviance: 1699.7  on 2060  degrees of freedom
    ## Residual deviance: 1694.1  on 2059  degrees of freedom
    ## AIC: 1698.1
    ## 
    ## Number of Fisher Scoring iterations: 4
    minUrine_glm <- glm(in_hospital_death ~ Urine_min, data=icu_patients_df1, family="binomial")
    summary(minUrine_glm) # is significant
    ## 
    ## Call:
    ## glm(formula = in_hospital_death ~ Urine_min, family = "binomial", 
    ##     data = icu_patients_df1)
    ## 
    ## Deviance Residuals: 
    ##     Min       1Q   Median       3Q      Max  
    ## -0.6034  -0.5952  -0.5631  -0.5105   2.9438  
    ## 
    ## Coefficients:
    ##              Estimate Std. Error z value Pr(>|z|)    
    ## (Intercept) -1.610937   0.076052 -21.182  < 2e-16 ***
    ## Urine_min   -0.006020   0.001787  -3.369 0.000756 ***
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ## 
    ## (Dispersion parameter for binomial family taken to be 1)
    ## 
    ##     Null deviance: 1699.7  on 2060  degrees of freedom
    ## Residual deviance: 1683.1  on 2059  degrees of freedom
    ## AIC: 1687.1
    ## 
    ## Number of Fisher Scoring iterations: 5
    minWBC_glm <- glm(in_hospital_death ~ WBC_min, data=icu_patients_df1, family="binomial")
    summary(minWBC_glm) # is significant
    ## 
    ## Call:
    ## glm(formula = in_hospital_death ~ WBC_min, family = "binomial", 
    ##     data = icu_patients_df1)
    ## 
    ## Deviance Residuals: 
    ##     Min       1Q   Median       3Q      Max  
    ## -1.2861  -0.5638  -0.5477  -0.5315   2.0563  
    ## 
    ## Coefficients:
    ##              Estimate Std. Error z value Pr(>|z|)    
    ## (Intercept) -1.987167   0.119356 -16.649   <2e-16 ***
    ## WBC_min      0.017452   0.008437   2.068   0.0386 *  
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ## 
    ## (Dispersion parameter for binomial family taken to be 1)
    ## 
    ##     Null deviance: 1699.7  on 2060  degrees of freedom
    ## Residual deviance: 1695.6  on 2059  degrees of freedom
    ## AIC: 1699.6
    ## 
    ## Number of Fisher Scoring iterations: 4
    maxWBC_glm <- glm(in_hospital_death ~ WBC_max, data=icu_patients_df1, family="binomial")
    summary(maxWBC_glm) # is significant
    ## 
    ## Call:
    ## glm(formula = in_hospital_death ~ WBC_max, family = "binomial", 
    ##     data = icu_patients_df1)
    ## 
    ## Deviance Residuals: 
    ##     Min       1Q   Median       3Q      Max  
    ## -1.2674  -0.5631  -0.5475  -0.5326   2.0545  
    ## 
    ## Coefficients:
    ##              Estimate Std. Error z value Pr(>|z|)    
    ## (Intercept) -1.982652   0.118080 -16.791   <2e-16 ***
    ## WBC_max      0.014086   0.006859   2.054     0.04 *  
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ## 
    ## (Dispersion parameter for binomial family taken to be 1)
    ## 
    ##     Null deviance: 1699.7  on 2060  degrees of freedom
    ## Residual deviance: 1695.7  on 2059  degrees of freedom
    ## AIC: 1699.7
    ## 
    ## Number of Fisher Scoring iterations: 4
    ### IN SUMMARY:
    # significant variables were:
      # age
      # ICUType
      # Weight_max
      # Albumin_min
      # Bilirubin_max
      # BUN_max
      # Creatinine_max
      # GCS_min
      # Glucose_max
      # HCO3_min
      # HR_max
      # Lactate_max
      # Na_min
      # NISysABP_min
      # pH_min
      # RespRate_min
      # RespRate_max
      # Temp_min
      # TroponinT_max
      # Urine_min
      # WBC_min
      # WBC_max
    
    # non-significant variables were:
      # Glucose_min
      # HR_min
      # K_min
      # K_max
      # MAP_min
      # Na_max
      # NISysABP_max
      # Platelets_min
      # PFratio
      # pH_max
      # Temp_max
      # TroponinI_max
    1. Fit an appropriate series of multivariable logistic regression models, justifying your approach. Assess each model you consider for goodness of fit and other relevant statistics.
    #################################################################################
    ### CODE COPIED FROM TASK 2
    ## Create a dataset without missing or invalid data to use to build the model ##
    ## in order to remain consistent and allow comparisons between models to be made ##
    
    
    # Check counts of missing data in each variable
    for(i in 1:length(colnames(icu_patients_df1))){
      print(c(i,colnames(icu_patients_df1[i]), sum(is.na(icu_patients_df1[i]))))
    }
    ## [1] "1"        "RecordID" "0"       
    ## [1] "2"              "Length_of_stay" "0"             
    ## [1] "3"     "SAPS1" "96"   
    ## [1] "4"    "SOFA" "0"   
    ## [1] "5"        "Survival" "1288"    
    ## [1] "6"                 "in_hospital_death" "0"                
    ## [1] "7"    "Days" "0"   
    ## [1] "8"      "Status" "0"     
    ## [1] "9"   "Age" "0"  
    ## [1] "10"           "Albumin_diff" "0"           
    ## [1] "11"          "Albumin_max" "0"          
    ## [1] "12"          "Albumin_min" "0"          
    ## [1] "13"       "ALP_diff" "0"       
    ## [1] "14"      "ALP_max" "0"      
    ## [1] "15"      "ALP_min" "0"      
    ## [1] "16"       "ALT_diff" "0"       
    ## [1] "17"      "ALT_max" "0"      
    ## [1] "18"      "ALT_min" "0"      
    ## [1] "19"       "AST_diff" "0"       
    ## [1] "20"      "AST_max" "0"      
    ## [1] "21"      "AST_min" "0"      
    ## [1] "22"             "Bilirubin_diff" "0"             
    ## [1] "23"            "Bilirubin_max" "0"            
    ## [1] "24"            "Bilirubin_min" "0"            
    ## [1] "25"       "BUN_diff" "0"       
    ## [1] "26"      "BUN_max" "0"      
    ## [1] "27"      "BUN_min" "0"      
    ## [1] "28"               "Cholesterol_diff" "0"               
    ## [1] "29"              "Cholesterol_max" "0"              
    ## [1] "30"              "Cholesterol_min" "0"              
    ## [1] "31"              "Creatinine_diff" "0"              
    ## [1] "32"             "Creatinine_max" "0"             
    ## [1] "33"             "Creatinine_min" "0"             
    ## [1] "34"           "DiasABP_diff" "715"         
    ## [1] "35"          "DiasABP_max" "715"        
    ## [1] "36"          "DiasABP_min" "715"        
    ## [1] "37"        "FiO2_diff" "0"        
    ## [1] "38"       "FiO2_max" "0"       
    ## [1] "39"       "FiO2_min" "0"       
    ## [1] "40"       "GCS_diff" "0"       
    ## [1] "41"      "GCS_max" "0"      
    ## [1] "42"      "GCS_min" "0"      
    ## [1] "43"     "Gender" "0"     
    ## [1] "44"           "Glucose_diff" "0"           
    ## [1] "45"          "Glucose_max" "0"          
    ## [1] "46"          "Glucose_min" "0"          
    ## [1] "47"        "HCO3_diff" "0"        
    ## [1] "48"       "HCO3_max" "0"       
    ## [1] "49"       "HCO3_min" "0"       
    ## [1] "50"       "HCT_diff" "0"       
    ## [1] "51"      "HCT_max" "0"      
    ## [1] "52"      "HCT_min" "0"      
    ## [1] "53"     "Height" "992"   
    ## [1] "54"      "HR_diff" "0"      
    ## [1] "55"     "HR_max" "0"     
    ## [1] "56"     "HR_min" "0"     
    ## [1] "57"      "ICUType" "0"      
    ## [1] "58"     "K_diff" "0"     
    ## [1] "59"    "K_max" "0"    
    ## [1] "60"    "K_min" "0"    
    ## [1] "61"           "Lactate_diff" "0"           
    ## [1] "62"          "Lactate_max" "0"          
    ## [1] "63"          "Lactate_min" "0"          
    ## [1] "64"       "MAP_diff" "0"       
    ## [1] "65"      "MAP_max" "0"      
    ## [1] "66"      "MAP_min" "0"      
    ## [1] "67"      "Mg_diff" "0"      
    ## [1] "68"     "Mg_max" "0"     
    ## [1] "69"     "Mg_min" "0"     
    ## [1] "70"      "Na_diff" "0"      
    ## [1] "71"     "Na_max" "0"     
    ## [1] "72"     "Na_min" "0"     
    ## [1] "73"             "NIDiasABP_diff" "455"           
    ## [1] "74"            "NIDiasABP_max" "455"          
    ## [1] "75"            "NIDiasABP_min" "455"          
    ## [1] "76"         "NIMAP_diff" "455"       
    ## [1] "77"        "NIMAP_max" "455"      
    ## [1] "78"        "NIMAP_min" "455"      
    ## [1] "79"            "NISysABP_diff" "453"          
    ## [1] "80"           "NISysABP_max" "453"         
    ## [1] "81"           "NISysABP_min" "453"         
    ## [1] "82"         "PaCO2_diff" "0"         
    ## [1] "83"        "PaCO2_max" "0"        
    ## [1] "84"        "PaCO2_min" "0"        
    ## [1] "85"        "PaO2_diff" "0"        
    ## [1] "86"       "PaO2_max" "0"       
    ## [1] "87"       "PaO2_min" "0"       
    ## [1] "88"      "pH_diff" "0"      
    ## [1] "89"     "pH_max" "0"     
    ## [1] "90"     "pH_min" "0"     
    ## [1] "91"             "Platelets_diff" "0"             
    ## [1] "92"            "Platelets_max" "0"            
    ## [1] "93"            "Platelets_min" "0"            
    ## [1] "94"            "RespRate_diff" "0"            
    ## [1] "95"           "RespRate_max" "0"           
    ## [1] "96"           "RespRate_min" "0"           
    ## [1] "97"        "SaO2_diff" "0"        
    ## [1] "98"       "SaO2_max" "0"       
    ## [1] "99"       "SaO2_min" "0"       
    ## [1] "100"         "SysABP_diff" "715"        
    ## [1] "101"        "SysABP_max" "715"       
    ## [1] "102"        "SysABP_min" "715"       
    ## [1] "103"       "Temp_diff" "0"        
    ## [1] "104"      "Temp_max" "0"       
    ## [1] "105"      "Temp_min" "0"       
    ## [1] "106"            "TroponinI_diff" "0"             
    ## [1] "107"           "TroponinI_max" "0"            
    ## [1] "108"           "TroponinI_min" "0"            
    ## [1] "109"            "TroponinT_diff" "0"             
    ## [1] "110"           "TroponinT_max" "0"            
    ## [1] "111"           "TroponinT_min" "0"            
    ## [1] "112"        "Urine_diff" "0"         
    ## [1] "113"       "Urine_max" "0"        
    ## [1] "114"       "Urine_min" "0"        
    ## [1] "115"      "WBC_diff" "0"       
    ## [1] "116"     "WBC_max" "0"      
    ## [1] "117"     "WBC_min" "0"      
    ## [1] "118"         "Weight_diff" "146"        
    ## [1] "119"        "Weight_max" "146"       
    ## [1] "120"        "Weight_min" "146"       
    ## [1] "121"     "PFratio" "0"
    ## Result: of the variables chosen to explore for the survival model, large amounts of missing data in:
    ##         Height (992), NISysABP_min (453), NISysABP_max (453), Weight_max (146)
    
    ## Decision: include Weight_max; remove Height, NISysABP_min, NISysABP_max
    
    
    # Check counts of negative data (noted some -1 values) in each variable
    for(i in 1:length(colnames(icu_patients_df1))){
      print(c(i,colnames(icu_patients_df1[i]), sum(icu_patients_df1[i] < 0)))
    }
    ## [1] "1"        "RecordID" "0"       
    ## [1] "2"              "Length_of_stay" "25"            
    ## [1] "3"     "SAPS1" NA     
    ## [1] "4"    "SOFA" "65"  
    ## [1] "5"        "Survival" NA        
    ## [1] "6"                 "in_hospital_death" "0"                
    ## [1] "7"    "Days" "0"   
    ## [1] "8"      "Status" "0"     
    ## [1] "9"   "Age" "0"  
    ## [1] "10"           "Albumin_diff" "0"           
    ## [1] "11"          "Albumin_max" "0"          
    ## [1] "12"          "Albumin_min" "0"          
    ## [1] "13"       "ALP_diff" "0"       
    ## [1] "14"      "ALP_max" "0"      
    ## [1] "15"      "ALP_min" "0"      
    ## [1] "16"       "ALT_diff" "0"       
    ## [1] "17"      "ALT_max" "0"      
    ## [1] "18"      "ALT_min" "0"      
    ## [1] "19"       "AST_diff" "0"       
    ## [1] "20"      "AST_max" "0"      
    ## [1] "21"      "AST_min" "0"      
    ## [1] "22"             "Bilirubin_diff" "0"             
    ## [1] "23"            "Bilirubin_max" "0"            
    ## [1] "24"            "Bilirubin_min" "0"            
    ## [1] "25"       "BUN_diff" "0"       
    ## [1] "26"      "BUN_max" "0"      
    ## [1] "27"      "BUN_min" "0"      
    ## [1] "28"               "Cholesterol_diff" "0"               
    ## [1] "29"              "Cholesterol_max" "0"              
    ## [1] "30"              "Cholesterol_min" "0"              
    ## [1] "31"              "Creatinine_diff" "0"              
    ## [1] "32"             "Creatinine_max" "0"             
    ## [1] "33"             "Creatinine_min" "0"             
    ## [1] "34"           "DiasABP_diff" NA            
    ## [1] "35"          "DiasABP_max" NA           
    ## [1] "36"          "DiasABP_min" NA           
    ## [1] "37"        "FiO2_diff" "0"        
    ## [1] "38"       "FiO2_max" "0"       
    ## [1] "39"       "FiO2_min" "0"       
    ## [1] "40"       "GCS_diff" "0"       
    ## [1] "41"      "GCS_max" "0"      
    ## [1] "42"      "GCS_min" "0"
    ## Warning in Ops.factor(left, right): '<' not meaningful for factors
    ## [1] "43"     "Gender" NA      
    ## [1] "44"           "Glucose_diff" "0"           
    ## [1] "45"          "Glucose_max" "0"          
    ## [1] "46"          "Glucose_min" "0"          
    ## [1] "47"        "HCO3_diff" "0"        
    ## [1] "48"       "HCO3_max" "0"       
    ## [1] "49"       "HCO3_min" "0"       
    ## [1] "50"       "HCT_diff" "0"       
    ## [1] "51"      "HCT_max" "0"      
    ## [1] "52"      "HCT_min" "0"      
    ## [1] "53"     "Height" NA      
    ## [1] "54"      "HR_diff" "0"      
    ## [1] "55"     "HR_max" "0"     
    ## [1] "56"     "HR_min" "0"
    ## Warning in Ops.factor(left, right): '<' not meaningful for factors
    ## [1] "57"      "ICUType" NA       
    ## [1] "58"     "K_diff" "0"     
    ## [1] "59"    "K_max" "0"    
    ## [1] "60"    "K_min" "0"    
    ## [1] "61"           "Lactate_diff" "0"           
    ## [1] "62"          "Lactate_max" "0"          
    ## [1] "63"          "Lactate_min" "0"          
    ## [1] "64"       "MAP_diff" "0"       
    ## [1] "65"      "MAP_max" "0"      
    ## [1] "66"      "MAP_min" "0"      
    ## [1] "67"      "Mg_diff" "0"      
    ## [1] "68"     "Mg_max" "0"     
    ## [1] "69"     "Mg_min" "0"     
    ## [1] "70"      "Na_diff" "0"      
    ## [1] "71"     "Na_max" "0"     
    ## [1] "72"     "Na_min" "0"     
    ## [1] "73"             "NIDiasABP_diff" NA              
    ## [1] "74"            "NIDiasABP_max" NA             
    ## [1] "75"            "NIDiasABP_min" NA             
    ## [1] "76"         "NIMAP_diff" NA          
    ## [1] "77"        "NIMAP_max" NA         
    ## [1] "78"        "NIMAP_min" NA         
    ## [1] "79"            "NISysABP_diff" NA             
    ## [1] "80"           "NISysABP_max" NA            
    ## [1] "81"           "NISysABP_min" NA            
    ## [1] "82"         "PaCO2_diff" "0"         
    ## [1] "83"        "PaCO2_max" "0"        
    ## [1] "84"        "PaCO2_min" "0"        
    ## [1] "85"        "PaO2_diff" "0"        
    ## [1] "86"       "PaO2_max" "0"       
    ## [1] "87"       "PaO2_min" "0"       
    ## [1] "88"      "pH_diff" "0"      
    ## [1] "89"     "pH_max" "0"     
    ## [1] "90"     "pH_min" "0"     
    ## [1] "91"             "Platelets_diff" "0"             
    ## [1] "92"            "Platelets_max" "0"            
    ## [1] "93"            "Platelets_min" "0"            
    ## [1] "94"            "RespRate_diff" "0"            
    ## [1] "95"           "RespRate_max" "0"           
    ## [1] "96"           "RespRate_min" "0"           
    ## [1] "97"        "SaO2_diff" "0"        
    ## [1] "98"       "SaO2_max" "0"       
    ## [1] "99"       "SaO2_min" "0"       
    ## [1] "100"         "SysABP_diff" NA           
    ## [1] "101"        "SysABP_max" NA          
    ## [1] "102"        "SysABP_min" NA          
    ## [1] "103"       "Temp_diff" "0"        
    ## [1] "104"      "Temp_max" "0"       
    ## [1] "105"      "Temp_min" "0"       
    ## [1] "106"            "TroponinI_diff" "0"             
    ## [1] "107"           "TroponinI_max" "0"            
    ## [1] "108"           "TroponinI_min" "0"            
    ## [1] "109"            "TroponinT_diff" "0"             
    ## [1] "110"           "TroponinT_max" "0"            
    ## [1] "111"           "TroponinT_min" "0"            
    ## [1] "112"        "Urine_diff" "0"         
    ## [1] "113"       "Urine_max" "0"        
    ## [1] "114"       "Urine_min" "0"        
    ## [1] "115"      "WBC_diff" "0"       
    ## [1] "116"     "WBC_max" "0"      
    ## [1] "117"     "WBC_min" "0"      
    ## [1] "118"         "Weight_diff" NA           
    ## [1] "119"        "Weight_max" NA          
    ## [1] "120"        "Weight_min" NA          
    ## [1] "121"     "PFratio" "0"
    ## Result: negative values in Length_of_stay and SOFA (not listed in initial choice of variables anyway)
    
    # Create a new dataset with the only non-missing data from list of initial variables chosen
    # (excluding those with very high missingness i.e. Height, NISysABP_min, NISysABP_max)
    nm_icu_model_df1 <- na.omit(subset(icu_patients_df1, 
                                       select=c(Days, Status, # the survival object variables
                                                RecordID, # keep record id for reference if needed
                                                in_hospital_death, # for task 1
                                                Age, Gender, ICUType, Weight_max,
                                                Albumin_min, Bilirubin_max,
                                                BUN_max, Creatinine_max, 
                                                GCS_max, Glucose_min, Glucose_max, 
                                                HCO3_min, HR_min, HR_max, K_min, 
                                                K_max, Lactate_max, MAP_min, Na_min,
                                                Na_max, Platelets_min, PFratio, pH_min,
                                                pH_max, RespRate_min, RespRate_max,
                                                Temp_min, Temp_max, TroponinT_max, 
                                                TroponinI_max, Urine_min, WBC_min, WBC_max)))
    ### CODE COPIED FROM TASK 2
    #################################################################################
    
    # all variables from initially selected predictors
    full_glm <- glm(in_hospital_death ~ 
                      Age + 
                      Gender + 
                      ICUType + 
                      Weight_max +
                      Albumin_min +
                      Bilirubin_max + 
                      BUN_max + 
                      Creatinine_max + 
                      GCS_max + 
                      Glucose_min + 
                      Glucose_max + 
                      HCO3_min +
                      HR_min + 
                      HR_max + 
                      K_min + 
                      K_max + 
                      Lactate_max + 
                      MAP_min + 
                      Na_min +
                      Na_max +
                      Platelets_min +
                      PFratio +
                      pH_min +
                      pH_max +
                      RespRate_min +
                      RespRate_max + 
                      Temp_min + 
                      Temp_max +
                      TroponinT_max +
                      TroponinI_max + 
                      Urine_min + 
                      WBC_min + 
                      WBC_max
                    ,data=nm_icu_model_df1, family="binomial")
    summary(full_glm) #AIC 1332.1
    ## 
    ## Call:
    ## glm(formula = in_hospital_death ~ Age + Gender + ICUType + Weight_max + 
    ##     Albumin_min + Bilirubin_max + BUN_max + Creatinine_max + 
    ##     GCS_max + Glucose_min + Glucose_max + HCO3_min + HR_min + 
    ##     HR_max + K_min + K_max + Lactate_max + MAP_min + Na_min + 
    ##     Na_max + Platelets_min + PFratio + pH_min + pH_max + RespRate_min + 
    ##     RespRate_max + Temp_min + Temp_max + TroponinT_max + TroponinI_max + 
    ##     Urine_min + WBC_min + WBC_max, family = "binomial", data = nm_icu_model_df1)
    ## 
    ## Deviance Residuals: 
    ##     Min       1Q   Median       3Q      Max  
    ## -2.0025  -0.5414  -0.3387  -0.1826   3.1551  
    ## 
    ## Coefficients:
    ##                                        Estimate Std. Error z value Pr(>|z|)    
    ## (Intercept)                          24.7550693 11.0324370   2.244 0.024842 *  
    ## Age                                   0.0355727  0.0055679   6.389 1.67e-10 ***
    ## GenderMale                           -0.0005774  0.1586626  -0.004 0.997097    
    ## ICUTypeCardiac Surgery Recovery Unit -1.1946684  0.3314631  -3.604 0.000313 ***
    ## ICUTypeMedical ICU                    0.1457551  0.2305142   0.632 0.527188    
    ## ICUTypeSurgical ICU                   0.1776610  0.2563794   0.693 0.488334    
    ## Weight_max                           -0.0041882  0.0037136  -1.128 0.259409    
    ## Albumin_min                          -0.3103087  0.1269198  -2.445 0.014488 *  
    ## Bilirubin_max                         0.0397973  0.0145689   2.732 0.006301 ** 
    ## BUN_max                               0.0218067  0.0041617   5.240 1.61e-07 ***
    ## Creatinine_max                       -0.0512660  0.0566167  -0.905 0.365204    
    ## GCS_max                              -0.1896782  0.0267396  -7.094 1.31e-12 ***
    ## Glucose_min                           0.0004277  0.0017341   0.247 0.805197    
    ## Glucose_max                           0.0005729  0.0010105   0.567 0.570710    
    ## HCO3_min                              0.0094985  0.0185570   0.512 0.608753    
    ## HR_min                                0.0110264  0.0057790   1.908 0.056391 .  
    ## HR_max                                0.0046164  0.0038442   1.201 0.229792    
    ## K_min                                -0.0801749  0.1621385  -0.494 0.620964    
    ## K_max                                -0.0707587  0.1016629  -0.696 0.486420    
    ## Lactate_max                           0.0645205  0.0365291   1.766 0.077350 .  
    ## MAP_min                              -0.0001513  0.0044240  -0.034 0.972727    
    ## Na_min                                0.0041071  0.0353159   0.116 0.907418    
    ## Na_max                               -0.0648695  0.0356990  -1.817 0.069198 .  
    ## Platelets_min                        -0.0009868  0.0008076  -1.222 0.221726    
    ## PFratio                              -0.0001635  0.0007894  -0.207 0.835900    
    ## pH_min                               -1.2268398  0.9477985  -1.294 0.195524    
    ## pH_max                               -0.1918512  1.4140768  -0.136 0.892080    
    ## RespRate_min                         -0.0231207  0.0254338  -0.909 0.363322    
    ## RespRate_max                          0.0138618  0.0122981   1.127 0.259680    
    ## Temp_min                             -0.1907196  0.0883748  -2.158 0.030922 *  
    ## Temp_max                             -0.0308143  0.1062282  -0.290 0.771758    
    ## TroponinT_max                         0.0188442  0.0354984   0.531 0.595525    
    ## TroponinI_max                        -0.0028271  0.0078796  -0.359 0.719758    
    ## Urine_min                            -0.0063152  0.0026190  -2.411 0.015897 *  
    ## WBC_min                               0.0656428  0.0277205   2.368 0.017883 *  
    ## WBC_max                              -0.0521569  0.0229737  -2.270 0.023190 *  
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ## 
    ## (Dispersion parameter for binomial family taken to be 1)
    ## 
    ##     Null deviance: 1604.2  on 1914  degrees of freedom
    ## Residual deviance: 1260.1  on 1879  degrees of freedom
    ## AIC: 1332.1
    ## 
    ## Number of Fisher Scoring iterations: 6
    ###
    # variables that were significant on univariate comparisons
    signifUni_glm <- glm(in_hospital_death ~
                           Age + 
                           ICUType + 
                           Weight_max +
                           Albumin_min + 
                           Bilirubin_max + 
                           BUN_max + 
                           Creatinine_max +
                           GCS_max + 
                           Glucose_max + 
                           HCO3_min + 
                           HR_max +
                           Lactate_max +
                           Na_min +
                           # NISysABP_min + this was removed from the na.omit part anyway
                           pH_min + 
                           RespRate_min +
                           RespRate_max +
                           Temp_min + 
                           TroponinT_max +
                           Urine_min +
                           WBC_min +
                           WBC_max
                         ,data=nm_icu_model_df1, family="binomial")
    summary(signifUni_glm) #AIC 1320.9
    ## 
    ## Call:
    ## glm(formula = in_hospital_death ~ Age + ICUType + Weight_max + 
    ##     Albumin_min + Bilirubin_max + BUN_max + Creatinine_max + 
    ##     GCS_max + Glucose_max + HCO3_min + HR_max + Lactate_max + 
    ##     Na_min + pH_min + RespRate_min + RespRate_max + Temp_min + 
    ##     TroponinT_max + Urine_min + WBC_min + WBC_max, family = "binomial", 
    ##     data = nm_icu_model_df1)
    ## 
    ## Deviance Residuals: 
    ##     Min       1Q   Median       3Q      Max  
    ## -1.9897  -0.5398  -0.3458  -0.1906   3.0306  
    ## 
    ## Coefficients:
    ##                                        Estimate Std. Error z value Pr(>|z|)    
    ## (Intercept)                           1.799e+01  6.567e+00   2.739 0.006157 ** 
    ## Age                                   3.404e-02  5.318e-03   6.401 1.55e-10 ***
    ## ICUTypeCardiac Surgery Recovery Unit -1.087e+00  3.073e-01  -3.538 0.000403 ***
    ## ICUTypeMedical ICU                    1.537e-01  2.259e-01   0.680 0.496226    
    ## ICUTypeSurgical ICU                   1.585e-01  2.470e-01   0.642 0.521184    
    ## Weight_max                           -3.417e-03  3.473e-03  -0.984 0.325245    
    ## Albumin_min                          -3.454e-01  1.223e-01  -2.824 0.004737 ** 
    ## Bilirubin_max                         4.376e-02  1.403e-02   3.120 0.001811 ** 
    ## BUN_max                               2.101e-02  3.916e-03   5.365 8.10e-08 ***
    ## Creatinine_max                       -6.020e-02  5.508e-02  -1.093 0.274450    
    ## GCS_max                              -1.781e-01  2.490e-02  -7.155 8.39e-13 ***
    ## Glucose_max                          -6.786e-07  7.610e-04  -0.001 0.999288    
    ## HCO3_min                              6.078e-03  1.765e-02   0.344 0.730494    
    ## HR_max                                7.162e-03  3.308e-03   2.165 0.030393 *  
    ## Lactate_max                           6.304e-02  3.494e-02   1.804 0.071235 .  
    ## Na_min                               -4.359e-02  1.467e-02  -2.972 0.002959 ** 
    ## pH_min                               -1.172e+00  8.056e-01  -1.455 0.145582    
    ## RespRate_min                         -1.761e-02  2.465e-02  -0.715 0.474870    
    ## RespRate_max                          1.419e-02  1.103e-02   1.287 0.198258    
    ## Temp_min                             -1.578e-01  7.993e-02  -1.974 0.048379 *  
    ## TroponinT_max                         1.198e-02  3.453e-02   0.347 0.728694    
    ## Urine_min                            -6.348e-03  2.574e-03  -2.467 0.013643 *  
    ## WBC_min                               6.828e-02  2.601e-02   2.625 0.008672 ** 
    ## WBC_max                              -6.037e-02  2.207e-02  -2.736 0.006225 ** 
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ## 
    ## (Dispersion parameter for binomial family taken to be 1)
    ## 
    ##     Null deviance: 1604.2  on 1914  degrees of freedom
    ## Residual deviance: 1272.9  on 1891  degrees of freedom
    ## AIC: 1320.9
    ## 
    ## Number of Fisher Scoring iterations: 6
    ###
    # variables that were significant in the full_glm
    signifFull_glm <- glm(in_hospital_death ~
                            Age + 
                            ICUType +
                            Albumin_min + 
                            Bilirubin_max + 
                            BUN_max + 
                            GCS_max + 
                            Temp_min + 
                            Urine_min + 
                            WBC_min + 
                            WBC_max
                          ,data=nm_icu_model_df1, family="binomial")
    summary(signifFull_glm) #AIC 1330.2
    ## 
    ## Call:
    ## glm(formula = in_hospital_death ~ Age + ICUType + Albumin_min + 
    ##     Bilirubin_max + BUN_max + GCS_max + Temp_min + Urine_min + 
    ##     WBC_min + WBC_max, family = "binomial", data = nm_icu_model_df1)
    ## 
    ## Deviance Residuals: 
    ##     Min       1Q   Median       3Q      Max  
    ## -1.8919  -0.5497  -0.3649  -0.2046   3.0349  
    ## 
    ## Coefficients:
    ##                                       Estimate Std. Error z value Pr(>|z|)    
    ## (Intercept)                           6.356911   2.698679   2.356  0.01849 *  
    ## Age                                   0.030984   0.004850   6.389 1.67e-10 ***
    ## ICUTypeCardiac Surgery Recovery Unit -1.206231   0.286775  -4.206 2.60e-05 ***
    ## ICUTypeMedical ICU                    0.065555   0.210415   0.312  0.75538    
    ## ICUTypeSurgical ICU                  -0.033654   0.229228  -0.147  0.88328    
    ## Albumin_min                          -0.380485   0.118054  -3.223  0.00127 ** 
    ## Bilirubin_max                         0.054089   0.013137   4.117 3.83e-05 ***
    ## BUN_max                               0.017585   0.002832   6.209 5.34e-10 ***
    ## GCS_max                              -0.179975   0.020954  -8.589  < 2e-16 ***
    ## Temp_min                             -0.201811   0.073755  -2.736  0.00621 ** 
    ## Urine_min                            -0.007162   0.002585  -2.770  0.00560 ** 
    ## WBC_min                               0.055865   0.024568   2.274  0.02297 *  
    ## WBC_max                              -0.044776   0.020492  -2.185  0.02889 *  
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ## 
    ## (Dispersion parameter for binomial family taken to be 1)
    ## 
    ##     Null deviance: 1604.2  on 1914  degrees of freedom
    ## Residual deviance: 1304.2  on 1902  degrees of freedom
    ## AIC: 1330.2
    ## 
    ## Number of Fisher Scoring iterations: 6
    # no missing data removed due to missingness
    
    # anova doesn't work because different missing data between the models
    anova(full_glm, signifUni_glm, test="Chisq") # the parameters different between the models are not significant
    ## Analysis of Deviance Table
    ## 
    ## Model 1: in_hospital_death ~ Age + Gender + ICUType + Weight_max + Albumin_min + 
    ##     Bilirubin_max + BUN_max + Creatinine_max + GCS_max + Glucose_min + 
    ##     Glucose_max + HCO3_min + HR_min + HR_max + K_min + K_max + 
    ##     Lactate_max + MAP_min + Na_min + Na_max + Platelets_min + 
    ##     PFratio + pH_min + pH_max + RespRate_min + RespRate_max + 
    ##     Temp_min + Temp_max + TroponinT_max + TroponinI_max + Urine_min + 
    ##     WBC_min + WBC_max
    ## Model 2: in_hospital_death ~ Age + ICUType + Weight_max + Albumin_min + 
    ##     Bilirubin_max + BUN_max + Creatinine_max + GCS_max + Glucose_max + 
    ##     HCO3_min + HR_max + Lactate_max + Na_min + pH_min + RespRate_min + 
    ##     RespRate_max + Temp_min + TroponinT_max + Urine_min + WBC_min + 
    ##     WBC_max
    ##   Resid. Df Resid. Dev  Df Deviance Pr(>Chi)
    ## 1      1879     1260.1                      
    ## 2      1891     1272.9 -12  -12.783    0.385
    anova(full_glm, signifFull_glm, test="Chisq") # the dropped parameters between the two models do matter
    ## Analysis of Deviance Table
    ## 
    ## Model 1: in_hospital_death ~ Age + Gender + ICUType + Weight_max + Albumin_min + 
    ##     Bilirubin_max + BUN_max + Creatinine_max + GCS_max + Glucose_min + 
    ##     Glucose_max + HCO3_min + HR_min + HR_max + K_min + K_max + 
    ##     Lactate_max + MAP_min + Na_min + Na_max + Platelets_min + 
    ##     PFratio + pH_min + pH_max + RespRate_min + RespRate_max + 
    ##     Temp_min + Temp_max + TroponinT_max + TroponinI_max + Urine_min + 
    ##     WBC_min + WBC_max
    ## Model 2: in_hospital_death ~ Age + ICUType + Albumin_min + Bilirubin_max + 
    ##     BUN_max + GCS_max + Temp_min + Urine_min + WBC_min + WBC_max
    ##   Resid. Df Resid. Dev  Df Deviance Pr(>Chi)   
    ## 1      1879     1260.1                         
    ## 2      1902     1304.2 -23  -44.154 0.005039 **
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ###
    # using the model with the lowest AIC
    # reduce it even further
    reduced_signifUni_glm <- step(signifUni_glm, trace=1)
    ## Start:  AIC=1320.87
    ## in_hospital_death ~ Age + ICUType + Weight_max + Albumin_min + 
    ##     Bilirubin_max + BUN_max + Creatinine_max + GCS_max + Glucose_max + 
    ##     HCO3_min + HR_max + Lactate_max + Na_min + pH_min + RespRate_min + 
    ##     RespRate_max + Temp_min + TroponinT_max + Urine_min + WBC_min + 
    ##     WBC_max
    ## 
    ##                  Df Deviance    AIC
    ## - Glucose_max     1   1272.9 1318.9
    ## - HCO3_min        1   1273.0 1319.0
    ## - TroponinT_max   1   1273.0 1319.0
    ## - RespRate_min    1   1273.4 1319.4
    ## - Weight_max      1   1273.9 1319.9
    ## - Creatinine_max  1   1274.1 1320.1
    ## - RespRate_max    1   1274.5 1320.5
    ## <none>                1272.9 1320.9
    ## - Lactate_max     1   1276.1 1322.1
    ## - pH_min          1   1276.6 1322.6
    ## - Temp_min        1   1276.9 1322.9
    ## - HR_max          1   1277.5 1323.5
    ## - WBC_min         1   1280.1 1326.1
    ## - Urine_min       1   1280.9 1326.9
    ## - WBC_max         1   1280.9 1326.9
    ## - Albumin_min     1   1280.9 1326.9
    ## - Na_min          1   1281.6 1327.6
    ## - Bilirubin_max   1   1282.3 1328.3
    ## - ICUType         3   1302.5 1344.5
    ## - BUN_max         1   1302.5 1348.5
    ## - Age             1   1318.7 1364.7
    ## - GCS_max         1   1325.1 1371.1
    ## 
    ## Step:  AIC=1318.87
    ## in_hospital_death ~ Age + ICUType + Weight_max + Albumin_min + 
    ##     Bilirubin_max + BUN_max + Creatinine_max + GCS_max + HCO3_min + 
    ##     HR_max + Lactate_max + Na_min + pH_min + RespRate_min + RespRate_max + 
    ##     Temp_min + TroponinT_max + Urine_min + WBC_min + WBC_max
    ## 
    ##                  Df Deviance    AIC
    ## - TroponinT_max   1   1273.0 1317.0
    ## - HCO3_min        1   1273.0 1317.0
    ## - RespRate_min    1   1273.4 1317.4
    ## - Weight_max      1   1273.9 1317.9
    ## - Creatinine_max  1   1274.1 1318.1
    ## - RespRate_max    1   1274.5 1318.5
    ## <none>                1272.9 1318.9
    ## - Lactate_max     1   1276.2 1320.2
    ## - pH_min          1   1276.6 1320.6
    ## - Temp_min        1   1276.9 1320.9
    ## - HR_max          1   1277.5 1321.5
    ## - WBC_min         1   1280.1 1324.1
    ## - Urine_min       1   1280.9 1324.9
    ## - WBC_max         1   1280.9 1324.9
    ## - Albumin_min     1   1281.0 1325.0
    ## - Na_min          1   1281.7 1325.7
    ## - Bilirubin_max   1   1282.4 1326.4
    ## - ICUType         3   1303.2 1343.2
    ## - BUN_max         1   1302.6 1346.6
    ## - Age             1   1318.8 1362.8
    ## - GCS_max         1   1325.3 1369.3
    ## 
    ## Step:  AIC=1316.99
    ## in_hospital_death ~ Age + ICUType + Weight_max + Albumin_min + 
    ##     Bilirubin_max + BUN_max + Creatinine_max + GCS_max + HCO3_min + 
    ##     HR_max + Lactate_max + Na_min + pH_min + RespRate_min + RespRate_max + 
    ##     Temp_min + Urine_min + WBC_min + WBC_max
    ## 
    ##                  Df Deviance    AIC
    ## - HCO3_min        1   1273.1 1315.1
    ## - RespRate_min    1   1273.5 1315.5
    ## - Weight_max      1   1274.0 1316.0
    ## - Creatinine_max  1   1274.2 1316.2
    ## - RespRate_max    1   1274.7 1316.7
    ## <none>                1273.0 1317.0
    ## - Lactate_max     1   1276.7 1318.7
    ## - Temp_min        1   1277.0 1319.0
    ## - pH_min          1   1277.1 1319.1
    ## - HR_max          1   1277.5 1319.5
    ## - WBC_min         1   1280.6 1322.6
    ## - Urine_min       1   1281.0 1323.0
    ## - Albumin_min     1   1281.2 1323.2
    ## - WBC_max         1   1281.4 1323.4
    ## - Na_min          1   1282.0 1324.0
    ## - Bilirubin_max   1   1282.9 1324.9
    ## - ICUType         3   1303.3 1341.3
    ## - BUN_max         1   1302.7 1344.7
    ## - Age             1   1318.8 1360.8
    ## - GCS_max         1   1325.5 1367.5
    ## 
    ## Step:  AIC=1315.11
    ## in_hospital_death ~ Age + ICUType + Weight_max + Albumin_min + 
    ##     Bilirubin_max + BUN_max + Creatinine_max + GCS_max + HR_max + 
    ##     Lactate_max + Na_min + pH_min + RespRate_min + RespRate_max + 
    ##     Temp_min + Urine_min + WBC_min + WBC_max
    ## 
    ##                  Df Deviance    AIC
    ## - RespRate_min    1   1273.6 1313.6
    ## - Weight_max      1   1274.1 1314.1
    ## - Creatinine_max  1   1274.4 1314.4
    ## - RespRate_max    1   1274.8 1314.8
    ## <none>                1273.1 1315.1
    ## - Lactate_max     1   1276.7 1316.7
    ## - Temp_min        1   1277.0 1317.0
    ## - pH_min          1   1277.1 1317.1
    ## - HR_max          1   1277.6 1317.6
    ## - WBC_min         1   1280.9 1320.9
    ## - Urine_min       1   1281.1 1321.1
    ## - Albumin_min     1   1281.2 1321.2
    ## - WBC_max         1   1281.9 1321.9
    ## - Na_min          1   1282.0 1322.0
    ## - Bilirubin_max   1   1283.2 1323.2
    ## - ICUType         3   1303.3 1339.3
    ## - BUN_max         1   1302.7 1342.7
    ## - Age             1   1319.3 1359.3
    ## - GCS_max         1   1325.5 1365.5
    ## 
    ## Step:  AIC=1313.62
    ## in_hospital_death ~ Age + ICUType + Weight_max + Albumin_min + 
    ##     Bilirubin_max + BUN_max + Creatinine_max + GCS_max + HR_max + 
    ##     Lactate_max + Na_min + pH_min + RespRate_max + Temp_min + 
    ##     Urine_min + WBC_min + WBC_max
    ## 
    ##                  Df Deviance    AIC
    ## - Weight_max      1   1274.6 1312.6
    ## - RespRate_max    1   1274.8 1312.8
    ## - Creatinine_max  1   1274.9 1312.9
    ## <none>                1273.6 1313.6
    ## - Lactate_max     1   1277.3 1315.3
    ## - pH_min          1   1277.4 1315.4
    ## - Temp_min        1   1277.7 1315.7
    ## - HR_max          1   1277.9 1315.9
    ## - Albumin_min     1   1281.5 1319.5
    ## - Urine_min       1   1281.6 1319.6
    ## - WBC_min         1   1281.8 1319.8
    ## - Na_min          1   1282.3 1320.3
    ## - WBC_max         1   1283.0 1321.0
    ## - Bilirubin_max   1   1284.3 1322.3
    ## - ICUType         3   1303.4 1337.4
    ## - BUN_max         1   1303.3 1341.3
    ## - Age             1   1319.3 1357.3
    ## - GCS_max         1   1329.8 1367.8
    ## 
    ## Step:  AIC=1312.62
    ## in_hospital_death ~ Age + ICUType + Albumin_min + Bilirubin_max + 
    ##     BUN_max + Creatinine_max + GCS_max + HR_max + Lactate_max + 
    ##     Na_min + pH_min + RespRate_max + Temp_min + Urine_min + WBC_min + 
    ##     WBC_max
    ## 
    ##                  Df Deviance    AIC
    ## - RespRate_max    1   1275.8 1311.8
    ## - Creatinine_max  1   1276.1 1312.1
    ## <none>                1274.6 1312.6
    ## - pH_min          1   1278.2 1314.2
    ## - Lactate_max     1   1278.3 1314.3
    ## - HR_max          1   1279.2 1315.2
    ## - Temp_min        1   1279.5 1315.5
    ## - Albumin_min     1   1282.3 1318.3
    ## - Urine_min       1   1282.7 1318.7
    ## - WBC_min         1   1282.8 1318.8
    ## - Na_min          1   1283.2 1319.2
    ## - WBC_max         1   1284.2 1320.2
    ## - Bilirubin_max   1   1285.2 1321.2
    ## - ICUType         3   1306.4 1338.4
    ## - BUN_max         1   1303.7 1339.7
    ## - Age             1   1326.6 1362.6
    ## - GCS_max         1   1330.3 1366.3
    ## 
    ## Step:  AIC=1311.85
    ## in_hospital_death ~ Age + ICUType + Albumin_min + Bilirubin_max + 
    ##     BUN_max + Creatinine_max + GCS_max + HR_max + Lactate_max + 
    ##     Na_min + pH_min + Temp_min + Urine_min + WBC_min + WBC_max
    ## 
    ##                  Df Deviance    AIC
    ## - Creatinine_max  1   1277.1 1311.1
    ## <none>                1275.8 1311.8
    ## - Lactate_max     1   1279.5 1313.5
    ## - pH_min          1   1279.6 1313.6
    ## - Temp_min        1   1280.3 1314.3
    ## - HR_max          1   1281.4 1315.4
    ## - Albumin_min     1   1283.1 1317.1
    ## - Na_min          1   1283.8 1317.8
    ## - Urine_min       1   1284.0 1318.0
    ## - WBC_min         1   1284.0 1318.0
    ## - WBC_max         1   1285.0 1319.0
    ## - Bilirubin_max   1   1288.6 1322.6
    ## - ICUType         3   1307.0 1337.0
    ## - BUN_max         1   1304.6 1338.6
    ## - Age             1   1327.0 1361.0
    ## - GCS_max         1   1342.9 1376.9
    ## 
    ## Step:  AIC=1311.11
    ## in_hospital_death ~ Age + ICUType + Albumin_min + Bilirubin_max + 
    ##     BUN_max + GCS_max + HR_max + Lactate_max + Na_min + pH_min + 
    ##     Temp_min + Urine_min + WBC_min + WBC_max
    ## 
    ##                 Df Deviance    AIC
    ## <none>               1277.1 1311.1
    ## - Lactate_max    1   1280.7 1312.7
    ## - pH_min         1   1280.8 1312.8
    ## - Temp_min       1   1281.5 1313.5
    ## - HR_max         1   1282.9 1314.9
    ## - Na_min         1   1284.5 1316.5
    ## - Urine_min      1   1284.7 1316.7
    ## - Albumin_min    1   1284.8 1316.8
    ## - WBC_min        1   1285.6 1317.6
    ## - WBC_max        1   1286.6 1318.6
    ## - Bilirubin_max  1   1289.6 1321.6
    ## - ICUType        3   1308.6 1336.6
    ## - BUN_max        1   1314.1 1346.1
    ## - Age            1   1333.1 1365.1
    ## - GCS_max        1   1344.1 1376.1
    # removed variables were:
      # Glucose_max
      # TroponinT_max
      # HCO3_min
      # RespRate_min
      # Weight_max
      # RespRate_max
      # Creatinine_max
    summary(reduced_signifUni_glm) # AIC 1311.1
    ## 
    ## Call:
    ## glm(formula = in_hospital_death ~ Age + ICUType + Albumin_min + 
    ##     Bilirubin_max + BUN_max + GCS_max + HR_max + Lactate_max + 
    ##     Na_min + pH_min + Temp_min + Urine_min + WBC_min + WBC_max, 
    ##     family = "binomial", data = nm_icu_model_df1)
    ## 
    ## Deviance Residuals: 
    ##     Min       1Q   Median       3Q      Max  
    ## -1.9438  -0.5450  -0.3479  -0.1945   2.9904  
    ## 
    ## Coefficients:
    ##                                       Estimate Std. Error z value Pr(>|z|)    
    ## (Intercept)                          16.771564   6.180202   2.714  0.00665 ** 
    ## Age                                   0.035748   0.005082   7.034 2.01e-12 ***
    ## ICUTypeCardiac Surgery Recovery Unit -1.107288   0.292041  -3.792  0.00015 ***
    ## ICUTypeMedical ICU                    0.138003   0.215368   0.641  0.52167    
    ## ICUTypeSurgical ICU                   0.123606   0.235752   0.524  0.60007    
    ## Albumin_min                          -0.330533   0.119828  -2.758  0.00581 ** 
    ## Bilirubin_max                         0.048073   0.013358   3.599  0.00032 ***
    ## BUN_max                               0.017653   0.002894   6.101 1.06e-09 ***
    ## GCS_max                              -0.177828   0.021643  -8.217  < 2e-16 ***
    ## HR_max                                0.007771   0.003215   2.417  0.01564 *  
    ## Lactate_max                           0.062615   0.033026   1.896  0.05797 .  
    ## Na_min                               -0.038723   0.014114  -2.744  0.00608 ** 
    ## pH_min                               -1.101299   0.756621  -1.456  0.14552    
    ## Temp_min                             -0.162389   0.078329  -2.073  0.03816 *  
    ## Urine_min                            -0.006031   0.002509  -2.404  0.01622 *  
    ## WBC_min                               0.072729   0.025587   2.842  0.00448 ** 
    ## WBC_max                              -0.063857   0.021592  -2.957  0.00310 ** 
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ## 
    ## (Dispersion parameter for binomial family taken to be 1)
    ## 
    ##     Null deviance: 1604.2  on 1914  degrees of freedom
    ## Residual deviance: 1277.1  on 1898  degrees of freedom
    ## AIC: 1311.1
    ## 
    ## Number of Fisher Scoring iterations: 6
    anova(reduced_signifUni_glm,signifUni_glm, test="Chisq") 
    ## Analysis of Deviance Table
    ## 
    ## Model 1: in_hospital_death ~ Age + ICUType + Albumin_min + Bilirubin_max + 
    ##     BUN_max + GCS_max + HR_max + Lactate_max + Na_min + pH_min + 
    ##     Temp_min + Urine_min + WBC_min + WBC_max
    ## Model 2: in_hospital_death ~ Age + ICUType + Weight_max + Albumin_min + 
    ##     Bilirubin_max + BUN_max + Creatinine_max + GCS_max + Glucose_max + 
    ##     HCO3_min + HR_max + Lactate_max + Na_min + pH_min + RespRate_min + 
    ##     RespRate_max + Temp_min + TroponinT_max + Urine_min + WBC_min + 
    ##     WBC_max
    ##   Resid. Df Resid. Dev Df Deviance Pr(>Chi)
    ## 1      1898     1277.1                     
    ## 2      1891     1272.9  7   4.2406   0.7517
    # p value not significant, the dropped parameters are not significant
    1. Present your final model. Your final model should not include all the predictor variables, just a small subset of them, which you have selected based on statistical significance and/or background knowledge.
    # same as model above: reduced_signifUni_glm
    finalICU_glm <- glm(in_hospital_death ~ 
                          Age +
                          ICUType + 
                          Albumin_min + 
                          Bilirubin_max +
                          BUN_max + 
                          GCS_max + 
                          HR_max + 
                          Lactate_max + 
                          Na_min + 
                          pH_min + 
                          Temp_min + 
                          Urine_min + 
                          WBC_min + 
                          WBC_max
                        ,data=nm_icu_model_df1, family="binomial")
    summary(finalICU_glm) # AIC 1311.1
    ## 
    ## Call:
    ## glm(formula = in_hospital_death ~ Age + ICUType + Albumin_min + 
    ##     Bilirubin_max + BUN_max + GCS_max + HR_max + Lactate_max + 
    ##     Na_min + pH_min + Temp_min + Urine_min + WBC_min + WBC_max, 
    ##     family = "binomial", data = nm_icu_model_df1)
    ## 
    ## Deviance Residuals: 
    ##     Min       1Q   Median       3Q      Max  
    ## -1.9438  -0.5450  -0.3479  -0.1945   2.9904  
    ## 
    ## Coefficients:
    ##                                       Estimate Std. Error z value Pr(>|z|)    
    ## (Intercept)                          16.771564   6.180202   2.714  0.00665 ** 
    ## Age                                   0.035748   0.005082   7.034 2.01e-12 ***
    ## ICUTypeCardiac Surgery Recovery Unit -1.107288   0.292041  -3.792  0.00015 ***
    ## ICUTypeMedical ICU                    0.138003   0.215368   0.641  0.52167    
    ## ICUTypeSurgical ICU                   0.123606   0.235752   0.524  0.60007    
    ## Albumin_min                          -0.330533   0.119828  -2.758  0.00581 ** 
    ## Bilirubin_max                         0.048073   0.013358   3.599  0.00032 ***
    ## BUN_max                               0.017653   0.002894   6.101 1.06e-09 ***
    ## GCS_max                              -0.177828   0.021643  -8.217  < 2e-16 ***
    ## HR_max                                0.007771   0.003215   2.417  0.01564 *  
    ## Lactate_max                           0.062615   0.033026   1.896  0.05797 .  
    ## Na_min                               -0.038723   0.014114  -2.744  0.00608 ** 
    ## pH_min                               -1.101299   0.756621  -1.456  0.14552    
    ## Temp_min                             -0.162389   0.078329  -2.073  0.03816 *  
    ## Urine_min                            -0.006031   0.002509  -2.404  0.01622 *  
    ## WBC_min                               0.072729   0.025587   2.842  0.00448 ** 
    ## WBC_max                              -0.063857   0.021592  -2.957  0.00310 ** 
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ## 
    ## (Dispersion parameter for binomial family taken to be 1)
    ## 
    ##     Null deviance: 1604.2  on 1914  degrees of freedom
    ## Residual deviance: 1277.1  on 1898  degrees of freedom
    ## AIC: 1311.1
    ## 
    ## Number of Fisher Scoring iterations: 6
    ### testing interactions
    
    # finalICU_glm_AgeCr = finalICU_glm + Age:Creatinine_max
    finalICU_glm_AgeCr <- glm(in_hospital_death ~ 
                          Age +
                          ICUType + 
                          Albumin_min + 
                          Bilirubin_max +
                          BUN_max + 
                          GCS_max + 
                          HR_max + 
                          Lactate_max + 
                          Na_min + 
                          pH_min + 
                          Temp_min + 
                          Urine_min + 
                          WBC_min + 
                          WBC_max +
                          
                          # interaction term  
                          Age:Creatinine_max # creatinine generally increases with age
                        , data=nm_icu_model_df1, family="binomial")
    summary(finalICU_glm_AgeCr) # AIC 1311.6
    ## 
    ## Call:
    ## glm(formula = in_hospital_death ~ Age + ICUType + Albumin_min + 
    ##     Bilirubin_max + BUN_max + GCS_max + HR_max + Lactate_max + 
    ##     Na_min + pH_min + Temp_min + Urine_min + WBC_min + WBC_max + 
    ##     Age:Creatinine_max, family = "binomial", data = nm_icu_model_df1)
    ## 
    ## Deviance Residuals: 
    ##     Min       1Q   Median       3Q      Max  
    ## -2.0058  -0.5441  -0.3471  -0.1923   3.0126  
    ## 
    ## Coefficients:
    ##                                        Estimate Std. Error z value Pr(>|z|)    
    ## (Intercept)                          17.2042718  6.2610209   2.748 0.005999 ** 
    ## Age                                   0.0364778  0.0051215   7.123 1.06e-12 ***
    ## ICUTypeCardiac Surgery Recovery Unit -1.1050590  0.2924687  -3.778 0.000158 ***
    ## ICUTypeMedical ICU                    0.1432747  0.2157226   0.664 0.506587    
    ## ICUTypeSurgical ICU                   0.1270050  0.2361028   0.538 0.590631    
    ## Albumin_min                          -0.3200195  0.1202310  -2.662 0.007775 ** 
    ## Bilirubin_max                         0.0482335  0.0133563   3.611 0.000305 ***
    ## BUN_max                               0.0207435  0.0038808   5.345 9.04e-08 ***
    ## GCS_max                              -0.1779749  0.0216652  -8.215  < 2e-16 ***
    ## HR_max                                0.0075795  0.0032185   2.355 0.018524 *  
    ## Lactate_max                           0.0634961  0.0330932   1.919 0.055022 .  
    ## Na_min                               -0.0404502  0.0141531  -2.858 0.004263 ** 
    ## pH_min                               -1.1307197  0.7701256  -1.468 0.142042    
    ## Temp_min                             -0.1627020  0.0784203  -2.075 0.038010 *  
    ## Urine_min                            -0.0064029  0.0025826  -2.479 0.013166 *  
    ## WBC_min                               0.0713769  0.0255692   2.792 0.005246 ** 
    ## WBC_max                              -0.0630659  0.0215458  -2.927 0.003422 ** 
    ## Age:Creatinine_max                   -0.0010441  0.0008793  -1.187 0.235047    
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ## 
    ## (Dispersion parameter for binomial family taken to be 1)
    ## 
    ##     Null deviance: 1604.2  on 1914  degrees of freedom
    ## Residual deviance: 1275.6  on 1897  degrees of freedom
    ## AIC: 1311.6
    ## 
    ## Number of Fisher Scoring iterations: 6
    # finalICU_glm_AgeTemp = finalICU_glm + Age:Temp_min
    finalICU_glm_AgeTemp <- glm(in_hospital_death ~ 
                          Age +
                          ICUType + 
                          Albumin_min + 
                          Bilirubin_max +
                          BUN_max + 
                          GCS_max + 
                          HR_max + 
                          Lactate_max + 
                          Na_min + 
                          pH_min + 
                          Temp_min + 
                          Urine_min + 
                          WBC_min + 
                          WBC_max +
                          
                          # interaction term  
                          Age:Temp_min # low temp more often associated with illness in the elderly e.g. cold sepsis
                        , data=nm_icu_model_df1, family="binomial")
    summary(finalICU_glm_AgeTemp) # AIC 1313.1
    ## 
    ## Call:
    ## glm(formula = in_hospital_death ~ Age + ICUType + Albumin_min + 
    ##     Bilirubin_max + BUN_max + GCS_max + HR_max + Lactate_max + 
    ##     Na_min + pH_min + Temp_min + Urine_min + WBC_min + WBC_max + 
    ##     Age:Temp_min, family = "binomial", data = nm_icu_model_df1)
    ## 
    ## Deviance Residuals: 
    ##     Min       1Q   Median       3Q      Max  
    ## -1.9443  -0.5449  -0.3478  -0.1945   2.9890  
    ## 
    ## Coefficients:
    ##                                       Estimate Std. Error z value Pr(>|z|)    
    ## (Intercept)                          16.295971  11.197145   1.455 0.145567    
    ## Age                                   0.042771   0.137985   0.310 0.756586    
    ## ICUTypeCardiac Surgery Recovery Unit -1.107832   0.292268  -3.790 0.000150 ***
    ## ICUTypeMedical ICU                    0.137945   0.215393   0.640 0.521891    
    ## ICUTypeSurgical ICU                   0.123568   0.235776   0.524 0.600216    
    ## Albumin_min                          -0.330377   0.119870  -2.756 0.005849 ** 
    ## Bilirubin_max                         0.048084   0.013358   3.600 0.000319 ***
    ## BUN_max                               0.017650   0.002894   6.098 1.07e-09 ***
    ## GCS_max                              -0.177900   0.021689  -8.202 2.36e-16 ***
    ## HR_max                                0.007774   0.003216   2.418 0.015615 *  
    ## Lactate_max                           0.062704   0.033071   1.896 0.057949 .  
    ## Na_min                               -0.038711   0.014117  -2.742 0.006103 ** 
    ## pH_min                               -1.101215   0.756691  -1.455 0.145585    
    ## Temp_min                             -0.149186   0.270756  -0.551 0.581637    
    ## Urine_min                            -0.006032   0.002509  -2.404 0.016222 *  
    ## WBC_min                               0.072782   0.025611   2.842 0.004486 ** 
    ## WBC_max                              -0.063901   0.021611  -2.957 0.003108 ** 
    ## Age:Temp_min                         -0.000196   0.003848  -0.051 0.959380    
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ## 
    ## (Dispersion parameter for binomial family taken to be 1)
    ## 
    ##     Null deviance: 1604.2  on 1914  degrees of freedom
    ## Residual deviance: 1277.1  on 1897  degrees of freedom
    ## AIC: 1313.1
    ## 
    ## Number of Fisher Scoring iterations: 6
    # finalICU_glm_AgeWeight = finalICU_glm + Age:Weight_max (rather than using Weight_min previously)
    finalICU_glm_AgeWeight <- glm(in_hospital_death ~ 
                          Age +
                          ICUType + 
                          Albumin_min + 
                          Bilirubin_max +
                          BUN_max + 
                          GCS_max + 
                          HR_max + 
                          Lactate_max + 
                          Na_min + 
                          pH_min + 
                          Temp_min + 
                          Urine_min + 
                          WBC_min + 
                          WBC_max +
                          
                          # interaction term  
                          Age:Weight_max # weight generally decreases with age
                        , data=nm_icu_model_df1, family="binomial")
    summary(finalICU_glm_AgeWeight) # AIC 1311
    ## 
    ## Call:
    ## glm(formula = in_hospital_death ~ Age + ICUType + Albumin_min + 
    ##     Bilirubin_max + BUN_max + GCS_max + HR_max + Lactate_max + 
    ##     Na_min + pH_min + Temp_min + Urine_min + WBC_min + WBC_max + 
    ##     Age:Weight_max, family = "binomial", data = nm_icu_model_df1)
    ## 
    ## Deviance Residuals: 
    ##     Min       1Q   Median       3Q      Max  
    ## -2.0043  -0.5467  -0.3475  -0.1917   3.0545  
    ## 
    ## Coefficients:
    ##                                        Estimate Std. Error z value Pr(>|z|)    
    ## (Intercept)                           1.710e+01  6.323e+00   2.704 0.006847 ** 
    ## Age                                   3.949e-02  5.739e-03   6.882 5.92e-12 ***
    ## ICUTypeCardiac Surgery Recovery Unit -1.068e+00  2.934e-01  -3.639 0.000273 ***
    ## ICUTypeMedical ICU                    1.308e-01  2.157e-01   0.607 0.544177    
    ## ICUTypeSurgical ICU                   1.330e-01  2.361e-01   0.563 0.573176    
    ## Albumin_min                          -3.363e-01  1.199e-01  -2.805 0.005039 ** 
    ## Bilirubin_max                         4.833e-02  1.338e-02   3.612 0.000304 ***
    ## BUN_max                               1.823e-02  2.924e-03   6.233 4.57e-10 ***
    ## GCS_max                              -1.790e-01  2.169e-02  -8.253  < 2e-16 ***
    ## HR_max                                7.452e-03  3.230e-03   2.307 0.021042 *  
    ## Lactate_max                           6.444e-02  3.315e-02   1.944 0.051930 .  
    ## Na_min                               -3.907e-02  1.409e-02  -2.772 0.005564 ** 
    ## pH_min                               -1.201e+00  7.874e-01  -1.525 0.127242    
    ## Temp_min                             -1.458e-01  7.896e-02  -1.846 0.064889 .  
    ## Urine_min                            -5.978e-03  2.507e-03  -2.384 0.017109 *  
    ## WBC_min                               7.239e-02  2.559e-02   2.829 0.004674 ** 
    ## WBC_max                              -6.299e-02  2.162e-02  -2.914 0.003568 ** 
    ## Age:Weight_max                       -7.005e-05  5.052e-05  -1.387 0.165553    
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ## 
    ## (Dispersion parameter for binomial family taken to be 1)
    ## 
    ##     Null deviance: 1604.2  on 1914  degrees of freedom
    ## Residual deviance: 1275.1  on 1897  degrees of freedom
    ## AIC: 1311.1
    ## 
    ## Number of Fisher Scoring iterations: 6
    # finalICU_glm_AgeAlbumin = finalICU_glm + Age:Albumin_min
    finalICU_glm_AgeAlbumin <- glm(in_hospital_death ~ 
                          Age +
                          ICUType + 
                          Albumin_min + 
                          Bilirubin_max +
                          BUN_max + 
                          GCS_max + 
                          HR_max + 
                          Lactate_max + 
                          Na_min + 
                          pH_min + 
                          Temp_min + 
                          Urine_min + 
                          WBC_min + 
                          WBC_max +
                          
                          # interaction term  
                          Age:Albumin_min # albumin generally decreases with age
                        , data=nm_icu_model_df1, family="binomial")
    summary(finalICU_glm_AgeAlbumin) # AIC 1309
    ## 
    ## Call:
    ## glm(formula = in_hospital_death ~ Age + ICUType + Albumin_min + 
    ##     Bilirubin_max + BUN_max + GCS_max + HR_max + Lactate_max + 
    ##     Na_min + pH_min + Temp_min + Urine_min + WBC_min + WBC_max + 
    ##     Age:Albumin_min, family = "binomial", data = nm_icu_model_df1)
    ## 
    ## Deviance Residuals: 
    ##     Min       1Q   Median       3Q      Max  
    ## -1.9359  -0.5523  -0.3464  -0.1840   3.0218  
    ## 
    ## Coefficients:
    ##                                       Estimate Std. Error z value Pr(>|z|)    
    ## (Intercept)                          19.347306   6.173815   3.134 0.001726 ** 
    ## Age                                  -0.004992   0.021570  -0.231 0.816990    
    ## ICUTypeCardiac Surgery Recovery Unit -1.101538   0.292134  -3.771 0.000163 ***
    ## ICUTypeMedical ICU                    0.125775   0.215780   0.583 0.559971    
    ## ICUTypeSurgical ICU                   0.125709   0.235844   0.533 0.594021    
    ## Albumin_min                          -1.355174   0.548435  -2.471 0.013474 *  
    ## Bilirubin_max                         0.048750   0.013410   3.635 0.000278 ***
    ## BUN_max                               0.017767   0.002897   6.133 8.62e-10 ***
    ## GCS_max                              -0.177107   0.021686  -8.167 3.16e-16 ***
    ## HR_max                                0.007565   0.003220   2.350 0.018782 *  
    ## Lactate_max                           0.062344   0.033194   1.878 0.060356 .  
    ## Na_min                               -0.037919   0.014226  -2.666 0.007687 ** 
    ## pH_min                               -1.070276   0.727151  -1.472 0.141054    
    ## Temp_min                             -0.164386   0.078641  -2.090 0.036588 *  
    ## Urine_min                            -0.005912   0.002509  -2.356 0.018449 *  
    ## WBC_min                               0.074097   0.025585   2.896 0.003778 ** 
    ## WBC_max                              -0.063696   0.021561  -2.954 0.003135 ** 
    ## Age:Albumin_min                       0.014583   0.007592   1.921 0.054741 .  
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ## 
    ## (Dispersion parameter for binomial family taken to be 1)
    ## 
    ##     Null deviance: 1604.2  on 1914  degrees of freedom
    ## Residual deviance: 1273.4  on 1897  degrees of freedom
    ## AIC: 1309.4
    ## 
    ## Number of Fisher Scoring iterations: 6
    # finalICU_glm_AgeICUType = finalICU_glm + Age:ICUType
    finalICU_glm_AgeICUType <- glm(in_hospital_death ~ 
                          Age +
                          ICUType + 
                          Albumin_min + 
                          Bilirubin_max +
                          BUN_max + 
                          GCS_max + 
                          HR_max + 
                          Lactate_max + 
                          Na_min + 
                          pH_min + 
                          Temp_min + 
                          Urine_min + 
                          WBC_min + 
                          WBC_max +
                          
                          # interaction term  
                          Age:ICUType # age is likely to be related to ICU type 
                                      # e.g. elderly more likely to have poor outcome 
                                      # after surgery requiring post-op ICU support
                        , data=nm_icu_model_df1, family="binomial")
    summary(finalICU_glm_AgeICUType) # AIC 1307
    ## 
    ## Call:
    ## glm(formula = in_hospital_death ~ Age + ICUType + Albumin_min + 
    ##     Bilirubin_max + BUN_max + GCS_max + HR_max + Lactate_max + 
    ##     Na_min + pH_min + Temp_min + Urine_min + WBC_min + WBC_max + 
    ##     Age:ICUType, family = "binomial", data = nm_icu_model_df1)
    ## 
    ## Deviance Residuals: 
    ##     Min       1Q   Median       3Q      Max  
    ## -1.9579  -0.5488  -0.3415  -0.1920   3.1057  
    ## 
    ## Coefficients:
    ##                                           Estimate Std. Error z value Pr(>|z|)
    ## (Intercept)                              17.858479   6.317804   2.827 0.004703
    ## Age                                       0.028563   0.015297   1.867 0.061863
    ## ICUTypeCardiac Surgery Recovery Unit     -0.137499   1.721588  -0.080 0.936343
    ## ICUTypeMedical ICU                        0.199901   1.243496   0.161 0.872284
    ## ICUTypeSurgical ICU                      -2.152542   1.365680  -1.576 0.114987
    ## Albumin_min                              -0.327271   0.121006  -2.705 0.006839
    ## Bilirubin_max                             0.047961   0.013482   3.557 0.000374
    ## BUN_max                                   0.018057   0.002897   6.232  4.6e-10
    ## GCS_max                                  -0.179741   0.021736  -8.269  < 2e-16
    ## HR_max                                    0.008283   0.003228   2.566 0.010299
    ## Lactate_max                               0.061953   0.033160   1.868 0.061719
    ## Na_min                                   -0.039643   0.014137  -2.804 0.005043
    ## pH_min                                   -1.121623   0.768555  -1.459 0.144457
    ## Temp_min                                 -0.170873   0.079380  -2.153 0.031350
    ## Urine_min                                -0.006144   0.002517  -2.441 0.014655
    ## WBC_min                                   0.072986   0.025797   2.829 0.004666
    ## WBC_max                                  -0.065673   0.021802  -3.012 0.002594
    ## Age:ICUTypeCardiac Surgery Recovery Unit -0.013777   0.023475  -0.587 0.557276
    ## Age:ICUTypeMedical ICU                   -0.001538   0.016578  -0.093 0.926097
    ## Age:ICUTypeSurgical ICU                   0.031959   0.018202   1.756 0.079123
    ##                                             
    ## (Intercept)                              ** 
    ## Age                                      .  
    ## ICUTypeCardiac Surgery Recovery Unit        
    ## ICUTypeMedical ICU                          
    ## ICUTypeSurgical ICU                         
    ## Albumin_min                              ** 
    ## Bilirubin_max                            ***
    ## BUN_max                                  ***
    ## GCS_max                                  ***
    ## HR_max                                   *  
    ## Lactate_max                              .  
    ## Na_min                                   ** 
    ## pH_min                                      
    ## Temp_min                                 *  
    ## Urine_min                                *  
    ## WBC_min                                  ** 
    ## WBC_max                                  ** 
    ## Age:ICUTypeCardiac Surgery Recovery Unit    
    ## Age:ICUTypeMedical ICU                      
    ## Age:ICUTypeSurgical ICU                  .  
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ## 
    ## (Dispersion parameter for binomial family taken to be 1)
    ## 
    ##     Null deviance: 1604.2  on 1914  degrees of freedom
    ## Residual deviance: 1266.9  on 1895  degrees of freedom
    ## AIC: 1306.9
    ## 
    ## Number of Fisher Scoring iterations: 6
    # Code from previous attempt at task 1
    # Gender:HCT, PaO2:RespRate not tested because they are not in the final model
    
    # Anova testing for the new models
    lapply(list(finalICU_glm_AgeCr, finalICU_glm_AgeTemp, finalICU_glm_AgeWeight,
                finalICU_glm_AgeAlbumin, finalICU_glm_AgeICUType), 
           function(x) {print(anova(finalICU_glm, x, test="Chisq"))} )
    ## Analysis of Deviance Table
    ## 
    ## Model 1: in_hospital_death ~ Age + ICUType + Albumin_min + Bilirubin_max + 
    ##     BUN_max + GCS_max + HR_max + Lactate_max + Na_min + pH_min + 
    ##     Temp_min + Urine_min + WBC_min + WBC_max
    ## Model 2: in_hospital_death ~ Age + ICUType + Albumin_min + Bilirubin_max + 
    ##     BUN_max + GCS_max + HR_max + Lactate_max + Na_min + pH_min + 
    ##     Temp_min + Urine_min + WBC_min + WBC_max + Age:Creatinine_max
    ##   Resid. Df Resid. Dev Df Deviance Pr(>Chi)
    ## 1      1898     1277.1                     
    ## 2      1897     1275.6  1   1.4776   0.2242
    ## Analysis of Deviance Table
    ## 
    ## Model 1: in_hospital_death ~ Age + ICUType + Albumin_min + Bilirubin_max + 
    ##     BUN_max + GCS_max + HR_max + Lactate_max + Na_min + pH_min + 
    ##     Temp_min + Urine_min + WBC_min + WBC_max
    ## Model 2: in_hospital_death ~ Age + ICUType + Albumin_min + Bilirubin_max + 
    ##     BUN_max + GCS_max + HR_max + Lactate_max + Na_min + pH_min + 
    ##     Temp_min + Urine_min + WBC_min + WBC_max + Age:Temp_min
    ##   Resid. Df Resid. Dev Df  Deviance Pr(>Chi)
    ## 1      1898     1277.1                      
    ## 2      1897     1277.1  1 0.0025966   0.9594
    ## Analysis of Deviance Table
    ## 
    ## Model 1: in_hospital_death ~ Age + ICUType + Albumin_min + Bilirubin_max + 
    ##     BUN_max + GCS_max + HR_max + Lactate_max + Na_min + pH_min + 
    ##     Temp_min + Urine_min + WBC_min + WBC_max
    ## Model 2: in_hospital_death ~ Age + ICUType + Albumin_min + Bilirubin_max + 
    ##     BUN_max + GCS_max + HR_max + Lactate_max + Na_min + pH_min + 
    ##     Temp_min + Urine_min + WBC_min + WBC_max + Age:Weight_max
    ##   Resid. Df Resid. Dev Df Deviance Pr(>Chi)
    ## 1      1898     1277.1                     
    ## 2      1897     1275.1  1   1.9802   0.1594
    ## Analysis of Deviance Table
    ## 
    ## Model 1: in_hospital_death ~ Age + ICUType + Albumin_min + Bilirubin_max + 
    ##     BUN_max + GCS_max + HR_max + Lactate_max + Na_min + pH_min + 
    ##     Temp_min + Urine_min + WBC_min + WBC_max
    ## Model 2: in_hospital_death ~ Age + ICUType + Albumin_min + Bilirubin_max + 
    ##     BUN_max + GCS_max + HR_max + Lactate_max + Na_min + pH_min + 
    ##     Temp_min + Urine_min + WBC_min + WBC_max + Age:Albumin_min
    ##   Resid. Df Resid. Dev Df Deviance Pr(>Chi)  
    ## 1      1898     1277.1                       
    ## 2      1897     1273.4  1   3.6995  0.05443 .
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ## Analysis of Deviance Table
    ## 
    ## Model 1: in_hospital_death ~ Age + ICUType + Albumin_min + Bilirubin_max + 
    ##     BUN_max + GCS_max + HR_max + Lactate_max + Na_min + pH_min + 
    ##     Temp_min + Urine_min + WBC_min + WBC_max
    ## Model 2: in_hospital_death ~ Age + ICUType + Albumin_min + Bilirubin_max + 
    ##     BUN_max + GCS_max + HR_max + Lactate_max + Na_min + pH_min + 
    ##     Temp_min + Urine_min + WBC_min + WBC_max + Age:ICUType
    ##   Resid. Df Resid. Dev Df Deviance Pr(>Chi)  
    ## 1      1898     1277.1                       
    ## 2      1895     1266.9  3   10.254  0.01653 *
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ## [[1]]
    ## Analysis of Deviance Table
    ## 
    ## Model 1: in_hospital_death ~ Age + ICUType + Albumin_min + Bilirubin_max + 
    ##     BUN_max + GCS_max + HR_max + Lactate_max + Na_min + pH_min + 
    ##     Temp_min + Urine_min + WBC_min + WBC_max
    ## Model 2: in_hospital_death ~ Age + ICUType + Albumin_min + Bilirubin_max + 
    ##     BUN_max + GCS_max + HR_max + Lactate_max + Na_min + pH_min + 
    ##     Temp_min + Urine_min + WBC_min + WBC_max + Age:Creatinine_max
    ##   Resid. Df Resid. Dev Df Deviance Pr(>Chi)
    ## 1      1898     1277.1                     
    ## 2      1897     1275.6  1   1.4776   0.2242
    ## 
    ## [[2]]
    ## Analysis of Deviance Table
    ## 
    ## Model 1: in_hospital_death ~ Age + ICUType + Albumin_min + Bilirubin_max + 
    ##     BUN_max + GCS_max + HR_max + Lactate_max + Na_min + pH_min + 
    ##     Temp_min + Urine_min + WBC_min + WBC_max
    ## Model 2: in_hospital_death ~ Age + ICUType + Albumin_min + Bilirubin_max + 
    ##     BUN_max + GCS_max + HR_max + Lactate_max + Na_min + pH_min + 
    ##     Temp_min + Urine_min + WBC_min + WBC_max + Age:Temp_min
    ##   Resid. Df Resid. Dev Df  Deviance Pr(>Chi)
    ## 1      1898     1277.1                      
    ## 2      1897     1277.1  1 0.0025966   0.9594
    ## 
    ## [[3]]
    ## Analysis of Deviance Table
    ## 
    ## Model 1: in_hospital_death ~ Age + ICUType + Albumin_min + Bilirubin_max + 
    ##     BUN_max + GCS_max + HR_max + Lactate_max + Na_min + pH_min + 
    ##     Temp_min + Urine_min + WBC_min + WBC_max
    ## Model 2: in_hospital_death ~ Age + ICUType + Albumin_min + Bilirubin_max + 
    ##     BUN_max + GCS_max + HR_max + Lactate_max + Na_min + pH_min + 
    ##     Temp_min + Urine_min + WBC_min + WBC_max + Age:Weight_max
    ##   Resid. Df Resid. Dev Df Deviance Pr(>Chi)
    ## 1      1898     1277.1                     
    ## 2      1897     1275.1  1   1.9802   0.1594
    ## 
    ## [[4]]
    ## Analysis of Deviance Table
    ## 
    ## Model 1: in_hospital_death ~ Age + ICUType + Albumin_min + Bilirubin_max + 
    ##     BUN_max + GCS_max + HR_max + Lactate_max + Na_min + pH_min + 
    ##     Temp_min + Urine_min + WBC_min + WBC_max
    ## Model 2: in_hospital_death ~ Age + ICUType + Albumin_min + Bilirubin_max + 
    ##     BUN_max + GCS_max + HR_max + Lactate_max + Na_min + pH_min + 
    ##     Temp_min + Urine_min + WBC_min + WBC_max + Age:Albumin_min
    ##   Resid. Df Resid. Dev Df Deviance Pr(>Chi)  
    ## 1      1898     1277.1                       
    ## 2      1897     1273.4  1   3.6995  0.05443 .
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ## 
    ## [[5]]
    ## Analysis of Deviance Table
    ## 
    ## Model 1: in_hospital_death ~ Age + ICUType + Albumin_min + Bilirubin_max + 
    ##     BUN_max + GCS_max + HR_max + Lactate_max + Na_min + pH_min + 
    ##     Temp_min + Urine_min + WBC_min + WBC_max
    ## Model 2: in_hospital_death ~ Age + ICUType + Albumin_min + Bilirubin_max + 
    ##     BUN_max + GCS_max + HR_max + Lactate_max + Na_min + pH_min + 
    ##     Temp_min + Urine_min + WBC_min + WBC_max + Age:ICUType
    ##   Resid. Df Resid. Dev Df Deviance Pr(>Chi)  
    ## 1      1898     1277.1                       
    ## 2      1895     1266.9  3   10.254  0.01653 *
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ## Result: borderline effect for age:albumin (p=0.054)
    ##         significant effect for age:icutype (p=0.016)
    
    
    # Input the significant interactions into the model
    finalICU_glm_interactions <- glm(in_hospital_death ~ 
                          Age +
                          ICUType + 
                          Albumin_min + 
                          Bilirubin_max +
                          BUN_max + 
                          GCS_max + 
                          HR_max + 
                          Lactate_max + 
                          Na_min + 
                          pH_min + 
                          Temp_min + 
                          Urine_min + 
                          WBC_min + 
                          WBC_max +
                          
                          # significant interaction terms
                          Age:ICUType + Age:Albumin_min
                        , data=nm_icu_model_df1, family="binomial")
    summary(finalICU_glm_interactions) # AIC 1305 (lowest so far - lower than just including age:icutype)
    ## 
    ## Call:
    ## glm(formula = in_hospital_death ~ Age + ICUType + Albumin_min + 
    ##     Bilirubin_max + BUN_max + GCS_max + HR_max + Lactate_max + 
    ##     Na_min + pH_min + Temp_min + Urine_min + WBC_min + WBC_max + 
    ##     Age:ICUType + Age:Albumin_min, family = "binomial", data = nm_icu_model_df1)
    ## 
    ## Deviance Residuals: 
    ##     Min       1Q   Median       3Q      Max  
    ## -1.9494  -0.5533  -0.3360  -0.1854   3.2388  
    ## 
    ## Coefficients:
    ##                                           Estimate Std. Error z value Pr(>|z|)
    ## (Intercept)                              20.855206   6.365565   3.276  0.00105
    ## Age                                      -0.018285   0.028752  -0.636  0.52480
    ## ICUTypeCardiac Surgery Recovery Unit     -0.562192   1.733448  -0.324  0.74570
    ## ICUTypeMedical ICU                       -0.243286   1.265623  -0.192  0.84756
    ## ICUTypeSurgical ICU                      -2.505360   1.374546  -1.823  0.06835
    ## Albumin_min                              -1.384342   0.567281  -2.440  0.01467
    ## Bilirubin_max                             0.048779   0.013523   3.607  0.00031
    ## BUN_max                                   0.018215   0.002902   6.276 3.47e-10
    ## GCS_max                                  -0.178502   0.021748  -8.208 2.26e-16
    ## HR_max                                    0.008056   0.003232   2.492  0.01269
    ## Lactate_max                               0.062277   0.033295   1.870  0.06142
    ## Na_min                                   -0.038919   0.014253  -2.731  0.00632
    ## pH_min                                   -1.084124   0.737653  -1.470  0.14164
    ## Temp_min                                 -0.172788   0.079499  -2.173  0.02974
    ## Urine_min                                -0.006015   0.002511  -2.395  0.01660
    ## WBC_min                                   0.074082   0.025771   2.875  0.00405
    ## WBC_max                                  -0.065411   0.021751  -3.007  0.00264
    ## Age:ICUTypeCardiac Surgery Recovery Unit -0.008024   0.023597  -0.340  0.73383
    ## Age:ICUTypeMedical ICU                    0.004228   0.016843   0.251  0.80181
    ## Age:ICUTypeSurgical ICU                   0.036583   0.018295   2.000  0.04554
    ## Age:Albumin_min                           0.014994   0.007834   1.914  0.05563
    ##                                             
    ## (Intercept)                              ** 
    ## Age                                         
    ## ICUTypeCardiac Surgery Recovery Unit        
    ## ICUTypeMedical ICU                          
    ## ICUTypeSurgical ICU                      .  
    ## Albumin_min                              *  
    ## Bilirubin_max                            ***
    ## BUN_max                                  ***
    ## GCS_max                                  ***
    ## HR_max                                   *  
    ## Lactate_max                              .  
    ## Na_min                                   ** 
    ## pH_min                                      
    ## Temp_min                                 *  
    ## Urine_min                                *  
    ## WBC_min                                  ** 
    ## WBC_max                                  ** 
    ## Age:ICUTypeCardiac Surgery Recovery Unit    
    ## Age:ICUTypeMedical ICU                      
    ## Age:ICUTypeSurgical ICU                  *  
    ## Age:Albumin_min                          .  
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ## 
    ## (Dispersion parameter for binomial family taken to be 1)
    ## 
    ##     Null deviance: 1604.2  on 1914  degrees of freedom
    ## Residual deviance: 1263.2  on 1894  degrees of freedom
    ## AIC: 1305.2
    ## 
    ## Number of Fisher Scoring iterations: 6

    Test some interaction terms based on clinical knowledge

    # 
    # #################################################################################
    # # TO BE DELETED FROM HERE
    # 
    # 
    # 
    # # based on clinical knowledge, test some interaction terms
    # # add one new term on top of finalICU_glm per model
    # # then compare models with interactions with baseline model
    # 
    # # finalICU_glm_2 = finalICU_glm + Age:Creatinine_max
    # finalICU_glm_2 <- glm(in_hospital_death ~ 
    #                       # significant predictors from step()
    #                       Age + SAPS1 + ICUType + Albumin_diff + Bilirubin_min + 
    #                       Bilirubin_diff + BUN_min + BUN_diff + Creatinine_max + 
    #                       GCS_max + Lactate_min + Na_min + Platelets_max + 
    #                       Temp_min + Urine_max + Urine_diff +
    #                       
    #                       # baseline demographics 
    #                       Gender + Length_of_stay + Weight_min + SOFA + 
    #                       
    #                       # other clinical relevance
    #                       Albumin_min + Glucose_max + HCT_min + HR_max +  PaO2_min +
    #                       PaCO2_min + pH_min + RespRate_max + TroponinT_max + 
    #                       WBC_max +
    #                       
    #                       # interaction term
    #                       + Age:Creatinine_max # creatinine generally increases with age
    #                      , data=icu_patients_df1, family="binomial")
    # 
    # # finalICU_glm_3 = finalICU_glm + Age:Temp_min
    # finalICU_glm_3 <- glm(in_hospital_death ~ 
    #                       # significant predictors from step()
    #                       Age + SAPS1 + ICUType + Albumin_diff + Bilirubin_min + 
    #                       Bilirubin_diff + BUN_min + BUN_diff + Creatinine_max + 
    #                       GCS_max + Lactate_min + Na_min + Platelets_max + 
    #                       Temp_min + Urine_max + Urine_diff +
    #                       
    #                       # baseline demographics 
    #                       Gender + Length_of_stay + Weight_min + SOFA + 
    #                       
    #                       # other clinical relevance
    #                       Albumin_min + Glucose_max + HCT_min + HR_max +  PaO2_min +
    #                       PaCO2_min + pH_min + RespRate_max + TroponinT_max + 
    #                       WBC_max +
    #                       
    #                       # interaction term
    #                       + Age:Temp_min # low temp more often associated with illness in the elderly e.g. cold sepsis
    #                      , data=icu_patients_df1, family="binomial")
    # 
    # # finalICU_glm_4 = finalICU_glm + Age:Weight_min
    # finalICU_glm_4 <- glm(in_hospital_death ~ 
    #                       # significant predictors from step()
    #                       Age + SAPS1 + ICUType + Albumin_diff + Bilirubin_min + 
    #                       Bilirubin_diff + BUN_min + BUN_diff + Creatinine_max + 
    #                       GCS_max + Lactate_min + Na_min + Platelets_max + 
    #                       Temp_min + Urine_max + Urine_diff +
    #                       
    #                       # baseline demographics 
    #                       Gender + Length_of_stay + Weight_min + SOFA + 
    #                       
    #                       # other clinical relevance
    #                       Albumin_min + Glucose_max + HCT_min + HR_max +  PaO2_min +
    #                       PaCO2_min + pH_min + RespRate_max + TroponinT_max + 
    #                       WBC_max +
    #                       
    #                       # interaction term
    #                       + Age:Weight_min # weight generally decreases with age
    #                      , data=icu_patients_df1, family="binomial")
    # 
    # # finalICU_glm_5 = finalICU_glm + Age:Albumin_min
    # finalICU_glm_5 <- glm(in_hospital_death ~ 
    #                       # significant predictors from step()
    #                       Age + SAPS1 + ICUType + Albumin_diff + Bilirubin_min + 
    #                       Bilirubin_diff + BUN_min + BUN_diff + Creatinine_max + 
    #                       GCS_max + Lactate_min + Na_min + Platelets_max + 
    #                       Temp_min + Urine_max + Urine_diff +
    #                       
    #                       # baseline demographics 
    #                       Gender + Length_of_stay + Weight_min + SOFA + 
    #                       
    #                       # other clinical relevance
    #                       Albumin_min + Glucose_max + HCT_min + HR_max +  PaO2_min +
    #                       PaCO2_min + pH_min + RespRate_max + TroponinT_max + 
    #                       WBC_max +
    #                       
    #                       # interaction term
    #                       Age:Albumin_min # albumin can decrease with age
    #                     , data=icu_patients_df1, family="binomial")
    # 
    # # finalICU_glm_6 = finalICU_glm + Gender:HCT_min
    # finalICU_glm_6 <- glm(in_hospital_death ~ 
    #                       # significant predictors from step()
    #                       Age + SAPS1 + ICUType + Albumin_diff + Bilirubin_min + 
    #                       Bilirubin_diff + BUN_min + BUN_diff + Creatinine_max + 
    #                       GCS_max + Lactate_min + Na_min + Platelets_max + 
    #                       Temp_min + Urine_max + Urine_diff +
    #                       
    #                       # baseline demographics 
    #                       Gender + Length_of_stay + Weight_min + SOFA + 
    #                       
    #                       # other clinical relevance
    #                       Albumin_min + Glucose_max + HCT_min + HR_max +  PaO2_min +
    #                       PaCO2_min + pH_min + RespRate_max + TroponinT_max + 
    #                       WBC_max +
    #                       
    #                       # interaction term
    #                       Gender:HCT_min # HCT can be lower in females than males
    #                     , data=icu_patients_df1, family="binomial")
    # 
    # # finalICU_glm_7 = finalICU_glm + PaO2_min:RespRate_max
    # finalICU_glm_7 <- glm(in_hospital_death ~ 
    #                       # significant predictors from step()
    #                       Age + SAPS1 + ICUType + Albumin_diff + Bilirubin_min + 
    #                       Bilirubin_diff + BUN_min + BUN_diff + Creatinine_max + 
    #                       GCS_max + Lactate_min + Na_min + Platelets_max + 
    #                       Temp_min + Urine_max + Urine_diff +
    #                       
    #                       # baseline demographics 
    #                       Gender + Length_of_stay + Weight_min + SOFA + 
    #                       
    #                       # other clinical relevance
    #                       Albumin_min + Glucose_max + HCT_min + HR_max +  PaO2_min +
    #                       PaCO2_min + pH_min + RespRate_max + TroponinT_max + 
    #                       WBC_max +
    #                       
    #                       # interaction term
    #                       PaO2_min:RespRate_max # PaO2 and resp rate are intrinsically related physiologically
    #                     , data=icu_patients_df1, family="binomial")
    # 
    # # finalICU_glm_8 = finalICU_glm + Age:ICUType
    # finalICU_glm_8 <- glm(in_hospital_death ~ 
    #                       # significant predictors from step()
    #                       Age + SAPS1 + ICUType + Albumin_diff + Bilirubin_min + 
    #                       Bilirubin_diff + BUN_min + BUN_diff + Creatinine_max + 
    #                       GCS_max + Lactate_min + Na_min + Platelets_max + 
    #                       Temp_min + Urine_max + Urine_diff +
    #                       
    #                       # baseline demographics 
    #                       Gender + Length_of_stay + Weight_min + SOFA + 
    #                       
    #                       # other clinical relevance
    #                       Albumin_min + Glucose_max + HCT_min + HR_max +  PaO2_min +
    #                       PaCO2_min + pH_min + RespRate_max + TroponinT_max + 
    #                       WBC_max +
    #                       
    #                       # interaction term
    #                       Age:ICUType # age is likely to be related to ICU type 
    #                                   # e.g. elderly more likely to have poor outcome after surgery requiring post-op ICU support
    #                     , data=icu_patients_df1, family="binomial")
    # 
    # 
    # # comparing models with anova
    # lapply(list(finalICU_glm_2, finalICU_glm_3, finalICU_glm_4, finalICU_glm_5,
    #             finalICU_glm_6, finalICU_glm_7, finalICU_glm_8), 
    #        function(x) {print(anova(finalICU_glm, x, test="Chisq"))} )
    #   # the effect of weight_min varied with age
    #   # the effect of ICUType varied with age
    #   # borderline -- the effect of resprate_max varied with PaO2_min
    # 
    # ## feel free to add other interactions to test
    # 
    # 
    # # input the significant interaction terms into a model and examine output
    # finalICU_glm_9 <- glm(in_hospital_death ~ 
    #                       # significant predictors from step()
    #                       Age + SAPS1 + ICUType + Albumin_diff + Bilirubin_min + 
    #                       Bilirubin_diff + BUN_min + BUN_diff + Creatinine_max + 
    #                       GCS_max + Lactate_min + Na_min + Platelets_max + 
    #                       Temp_min + Urine_max + Urine_diff +
    #                       
    #                       # baseline demographics 
    #                       Gender + Length_of_stay + Weight_min + SOFA + 
    #                       
    #                       # other clinical relevance
    #                       Albumin_min + Glucose_max + HCT_min + HR_max +  PaO2_min +
    #                       PaCO2_min + pH_min + RespRate_max + TroponinT_max + 
    #                       WBC_max +
    #                       
    #                       # interaction terms
    #                       Age:Weight_min + Age:ICUType # effects that had a significant effect on the model with anova
    #                     , data=icu_patients_df1, family="binomial")
    # 
    # summary(finalICU_glm_9)
    # # the AIC is slightly lower than finalICU_glm
    # 
    # ## the effects of the interactions have significance but the ORs are close to 1 with narrow CIs -- perhaps not very clinically informative (i.e. the odds are essentially 1 i.e. equal)
    # options(scipen=999)
    # exp(coef(finalICU_glm_9))
    # exp(confint(finalICU_glm_9))
    
    # TO BE DELETD FROM ABOVE TO HERE
    #################################################################################

    Testing the modified poisson regression, as the outcome is 14% in this data (>10% - common)

    #################################################################################
    # NEED TO DECIDE WHETHER TO INCLUDE THIS SECTION
    
    # test using modified poisson regression for more common outcomes on the same covariates as above
    
    finalICU_glm_poisson <- glm(in_hospital_death ~ 
                          # significant predictors from step()
                          Age + SAPS1 + ICUType + Albumin_diff + Bilirubin_min + 
                          Bilirubin_diff + BUN_min + BUN_diff + Creatinine_max + 
                          GCS_max + Lactate_min + Na_min + Platelets_max + 
                          Temp_min + Urine_max + Urine_diff +
                            
                          # baseline demographics should be included even if not significant
                          Gender + Length_of_stay + Weight_min + 
                          SOFA + # an indicator of how well SOFA score determines mortality independent to its components
                          
                          # other clinical relevance
                          Albumin_min + # low albumin indicates malnutrition or liver failure
                          Glucose_max + # hyperglycaemia is a stress response
                          HCT_min + # low HCT = anaemia
                          HR_max + # tachycardia may indicate septic shock / inflammation
                          PaO2_min + # hypoxia = inadequate organ perfusion/oxygenation
                          PaCO2_min + #hypercapnia = respiratory / ventilation failure
                          pH_min + # indicates acidaemia / inadequate organ perfusion
                          RespRate_max + # indicates respiratory failure
                          TroponinT_max + # indicates myocardial damage
                          WBC_max # indicates infection
                          
                        , data=icu_patients_df1, family="poisson"(link="log"))
    
    summary(finalICU_glm_poisson)
    ## 
    ## Call:
    ## glm(formula = in_hospital_death ~ Age + SAPS1 + ICUType + Albumin_diff + 
    ##     Bilirubin_min + Bilirubin_diff + BUN_min + BUN_diff + Creatinine_max + 
    ##     GCS_max + Lactate_min + Na_min + Platelets_max + Temp_min + 
    ##     Urine_max + Urine_diff + Gender + Length_of_stay + Weight_min + 
    ##     SOFA + Albumin_min + Glucose_max + HCT_min + HR_max + PaO2_min + 
    ##     PaCO2_min + pH_min + RespRate_max + TroponinT_max + WBC_max, 
    ##     family = poisson(link = "log"), data = icu_patients_df1)
    ## 
    ## Deviance Residuals: 
    ##     Min       1Q   Median       3Q      Max  
    ## -1.8744  -0.5069  -0.3491  -0.2183   2.4834  
    ## 
    ## Coefficients:
    ##                                        Estimate Std. Error z value Pr(>|z|)    
    ## (Intercept)                           5.0214843  3.3904946   1.481  0.13859    
    ## Age                                   0.0198792  0.0049400   4.024 5.72e-05 ***
    ## SAPS1                                 0.0339633  0.0204016   1.665  0.09596 .  
    ## ICUTypeCardiac Surgery Recovery Unit -0.7603505  0.2813563  -2.702  0.00688 ** 
    ## ICUTypeMedical ICU                    0.0629493  0.1935242   0.325  0.74497    
    ## ICUTypeSurgical ICU                   0.1931383  0.2185759   0.884  0.37690    
    ## Albumin_diff                          0.1457395  0.1641374   0.888  0.37459    
    ## Bilirubin_min                         0.1464095  0.0568473   2.575  0.01001 *  
    ## Bilirubin_diff                       -0.1263382  0.0579171  -2.181  0.02916 *  
    ## BUN_min                               0.0292204  0.0068460   4.268 1.97e-05 ***
    ## BUN_diff                             -0.0157550  0.0068983  -2.284  0.02238 *  
    ## Creatinine_max                       -0.0890083  0.0548536  -1.623  0.10466    
    ## GCS_max                              -0.0990101  0.0213334  -4.641 3.47e-06 ***
    ## Lactate_min                          -0.0110473  0.0333359  -0.331  0.74035    
    ## Na_min                               -0.0352725  0.0121226  -2.910  0.00362 ** 
    ## Platelets_max                        -0.0006707  0.0006484  -1.034  0.30096    
    ## Temp_min                             -0.0647282  0.0531798  -1.217  0.22354    
    ## Urine_max                            -0.0015792  0.0014410  -1.096  0.27312    
    ## Urine_diff                            0.0011907  0.0015125   0.787  0.43113    
    ## GenderMale                           -0.0834178  0.1320252  -0.632  0.52750    
    ## Length_of_stay                       -0.0042229  0.0048572  -0.869  0.38462    
    ## Weight_min                           -0.0037488  0.0033072  -1.134  0.25700    
    ## SOFA                                  0.0144047  0.0215427   0.669  0.50371    
    ## Albumin_min                          -0.1336429  0.1048927  -1.274  0.20263    
    ## Glucose_max                           0.0001538  0.0006267   0.245  0.80608    
    ## HCT_min                              -0.0108434  0.0126736  -0.856  0.39222    
    ## HR_max                                0.0052571  0.0026488   1.985  0.04718 *  
    ## PaO2_min                              0.0004131  0.0011102   0.372  0.70981    
    ## PaCO2_min                             0.0059266  0.0079216   0.748  0.45437    
    ## pH_min                               -0.0847659  0.2631944  -0.322  0.74740    
    ## RespRate_max                          0.0095491  0.0085073   1.122  0.26167    
    ## TroponinT_max                         0.0334174  0.0247510   1.350  0.17697    
    ## WBC_max                              -0.0071252  0.0086893  -0.820  0.41222    
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ## 
    ## (Dispersion parameter for poisson family taken to be 1)
    ## 
    ##     Null deviance: 1046.23  on 1854  degrees of freedom
    ## Residual deviance:  769.47  on 1822  degrees of freedom
    ##   (206 observations deleted due to missingness)
    ## AIC: 1381.5
    ## 
    ## Number of Fisher Scoring iterations: 6
    # fewer significant variables (likely as CI can be wider in poisson)
    # but the variables that are significant were also significant in the logistic model
    
    # examine ORs from logistic regression
    options(scipen=999) # turn off scientific notation
    exp(coef(finalICU_glm_interactions))
    ##                              (Intercept) 
    ##                      1141039705.79856825 
    ##                                      Age 
    ##                               0.98188117 
    ##     ICUTypeCardiac Surgery Recovery Unit 
    ##                               0.56995835 
    ##                       ICUTypeMedical ICU 
    ##                               0.78404694 
    ##                      ICUTypeSurgical ICU 
    ##                               0.08164616 
    ##                              Albumin_min 
    ##                               0.25048853 
    ##                            Bilirubin_max 
    ##                               1.04998791 
    ##                                  BUN_max 
    ##                               1.01838146 
    ##                                  GCS_max 
    ##                               0.83652254 
    ##                                   HR_max 
    ##                               1.00808840 
    ##                              Lactate_max 
    ##                               1.06425731 
    ##                                   Na_min 
    ##                               0.96182843 
    ##                                   pH_min 
    ##                               0.33819783 
    ##                                 Temp_min 
    ##                               0.84131613 
    ##                                Urine_min 
    ##                               0.99400267 
    ##                                  WBC_min 
    ##                               1.07689505 
    ##                                  WBC_max 
    ##                               0.93668260 
    ## Age:ICUTypeCardiac Surgery Recovery Unit 
    ##                               0.99200823 
    ##                   Age:ICUTypeMedical ICU 
    ##                               1.00423652 
    ##                  Age:ICUTypeSurgical ICU 
    ##                               1.03725988 
    ##                          Age:Albumin_min 
    ##                               1.01510738
    # examine RRs from logistic regression
    exp(coef(finalICU_glm_poisson))
    ##                          (Intercept)                                  Age 
    ##                          151.6362129                            1.0200782 
    ##                                SAPS1 ICUTypeCardiac Surgery Recovery Unit 
    ##                            1.0345467                            0.4675026 
    ##                   ICUTypeMedical ICU                  ICUTypeSurgical ICU 
    ##                            1.0649728                            1.2130505 
    ##                         Albumin_diff                        Bilirubin_min 
    ##                            1.1568947                            1.1576701 
    ##                       Bilirubin_diff                              BUN_min 
    ##                            0.8813167                            1.0296515 
    ##                             BUN_diff                       Creatinine_max 
    ##                            0.9843684                            0.9148380 
    ##                              GCS_max                          Lactate_min 
    ##                            0.9057335                            0.9890134 
    ##                               Na_min                        Platelets_max 
    ##                            0.9653423                            0.9993295 
    ##                             Temp_min                            Urine_max 
    ##                            0.9373222                            0.9984220 
    ##                           Urine_diff                           GenderMale 
    ##                            1.0011914                            0.9199667 
    ##                       Length_of_stay                           Weight_min 
    ##                            0.9957860                            0.9962582 
    ##                                 SOFA                          Albumin_min 
    ##                            1.0145089                            0.8749024 
    ##                          Glucose_max                              HCT_min 
    ##                            1.0001539                            0.9892151 
    ##                               HR_max                             PaO2_min 
    ##                            1.0052709                            1.0004132 
    ##                            PaCO2_min                               pH_min 
    ##                            1.0059442                            0.9187274 
    ##                         RespRate_max                        TroponinT_max 
    ##                            1.0095948                            1.0339820 
    ##                              WBC_max 
    ##                            0.9929001
    # the ORs and RRs appear very similar --> check the actual differences
    exp(coef(finalICU_glm_interactions))-exp(coef(finalICU_glm_poisson))
    ## Warning in exp(coef(finalICU_glm_interactions)) -
    ## exp(coef(finalICU_glm_poisson)): longer object length is not a multiple of
    ## shorter object length
    ##                          (Intercept)                                  Age 
    ##                1141039554.1623554230                        -0.0381969906 
    ##                                SAPS1 ICUTypeCardiac Surgery Recovery Unit 
    ##                        -0.4645883206                         0.3165443793 
    ##                   ICUTypeMedical ICU                  ICUTypeSurgical ICU 
    ##                        -0.9833266666                        -0.9625620124 
    ##                         Albumin_diff                        Bilirubin_min 
    ##                        -0.1069068314                        -0.1392886834 
    ##                       Bilirubin_diff                              BUN_min 
    ##                        -0.0447941859                        -0.0215631185 
    ##                             BUN_diff                       Creatinine_max 
    ##                         0.0798888748                         0.0469904430 
    ##                              GCS_max                          Lactate_min 
    ##                        -0.5675356972                        -0.1476973160 
    ##                               Na_min                        Platelets_max 
    ##                         0.0286603803                         0.0775655574 
    ##                             Temp_min                            Urine_max 
    ##                        -0.0006395689                        -0.0064138009 
    ##                           Urine_diff                           GenderMale 
    ##                         0.0030450858                         0.1172931629 
    ##                       Length_of_stay                           Weight_min 
    ##                         0.0193214104                1141039704.8023099899 
    ##                                 SOFA                          Albumin_min 
    ##                        -0.0326277521                        -0.3049440765 
    ##                          Glucose_max                              HCT_min 
    ##                        -0.2161069212                        -0.9075689683 
    ##                               HR_max                             PaO2_min 
    ##                        -0.7547823984                         0.0495747182 
    ##                            PaCO2_min                               pH_min 
    ##                         0.0124372203                        -0.0822048140 
    ##                         RespRate_max                        TroponinT_max 
    ##                        -0.0015063952                         0.0302753110 
    ##                              WBC_max 
    ##                        -0.0310717102
    # the intercept is very different (by 82000!) - not sure how to interpret that. the other estimates are very similar
    
    # perhaps the logistic model is therefore justified? just need to be careful in interpretation using 'odds' rather than 'risk'
    
    #################################################################################
    1. For your final model, present a set of diagnostic statistics and/or charts and comment on them.
    library(magrittr)
    library(dplyr)
    ## 
    ## Attaching package: 'dplyr'
    ## The following object is masked from 'package:gridExtra':
    ## 
    ##     combine
    ## The following objects are masked from 'package:stats':
    ## 
    ##     filter, lag
    ## The following objects are masked from 'package:base':
    ## 
    ##     intersect, setdiff, setequal, union
    ### Goodness of fit using bins df1 ###
    
    # add predicted probabilities to the data frame
    nm_icu_model_df1 %>% mutate(predprob=predict(finalICU_glm_interactions, type="response"),
                       linpred=predict(finalICU_glm_interactions)) %>%
    # group the data into bins based on the linear predictor fitted values
    group_by(cut(linpred, breaks=unique(quantile(linpred, (1:50)/51)))) %>%
    # summarise by bin
    summarise(death_bin=sum(in_hospital_death), predprob_bin=mean(predprob), n_bin=n()) %>%
    # add the standard error of the mean predicted probaility for each bin
    mutate(se_predprob_bin=sqrt(predprob_bin*(1 - predprob_bin)/n_bin)) %>%
    # plot it with 95% confidence interval bars
    ggplot(aes(x=predprob_bin, 
               y=death_bin/n_bin, 
               ymin=death_bin/n_bin - 1.96*se_predprob_bin,
               ymax=death_bin/n_bin + 1.96*se_predprob_bin)) +
      geom_point() + geom_linerange(colour="orange", alpha=0.4) +
      geom_abline(intercept=0, slope=1) + 
      labs(x="Predicted probability (binned)",
           y="Observed proportion (in each bin)")

    # the ideal calibration line fits within most of the dots and their 95% CI
    
    ### Goodness of fit using Hosmer Lemeshow stat ###
    
    nm_icu_model_df1 %>% mutate(predprob=predict(finalICU_glm_interactions, type="response"),
                       linpred=predict(finalICU_glm_interactions)) %>%
    group_by(cut(linpred, breaks=unique(quantile(linpred, (1:50)/51)))) %>%
    summarise(death_bin=sum(in_hospital_death), predprob_bin=mean(predprob), n_bin=n()) %>%
    mutate(se_predprob_bin=sqrt(predprob_bin*(1 - predprob_bin)/n_bin)) -> hl_df
    
    hl_stat <- with(hl_df, sum( (death_bin - n_bin*predprob_bin)^2 /
                                (n_bin* predprob_bin*(1 - predprob_bin))))
    hl <- c(hosmer_lemeshow_stat=hl_stat, hl_degrees_freedom=nrow(hl_df) - 1)
    hl
    ## hosmer_lemeshow_stat   hl_degrees_freedom 
    ##             51.77871             49.00000
    # calculate p-value
    c(p_val=1 - pchisq(hl[1], hl[2])) # the p value here is not statistically significant, indicating no lack of fit
    ## p_val.hosmer_lemeshow_stat 
    ##                  0.3659299
    ### Brier score ###
    
    get_brier <- function(model){
      predprob <- predict(model, type="response")
      Brier_score <- mean((predprob - nm_icu_model_df1$in_hospital_death)^2)
      return(Brier_score)
    }
    
    get_brier(finalICU_glm)
    ## [1] 0.1022154
    get_brier(finalICU_glm_interactions)
    ## [1] 0.1012639
    # the final model with interactions has slightly lower brier score -> lower score is better fit
    
    
    
    
    ### trying to fit our model to icu_patients_df0 data ###
    ### Commented out for now, in order to test knitting the file ###
    
    # icu_patients_df0
    # alot of missing data here also!
    # for(i in 1:length(colnames(icu_patients_df0))){
    #   print(c(i,colnames(icu_patients_df0[i]), sum(is.na(icu_patients_df0[i]))))
    # }
    # 
    # # remove columns with too much missing data
    # # arbitrary selection of >200
    # # albumin, ALP, ALT, AST, bilirubin, cholesterol, diasABP, FiO2, lactate, MAP, NIDiasABP, NIMAP, NISSysABP
    # # pH, RespRate, SaO2, Troponin
    # 
    # icu_patients_df0_nm <- icu_patients_df0[, -c(10:24, 28:30, 34:39, 61:66, 73:90, 94:102, 106:111 )]
    # icu_patients_df0_nm <- na.omit(icu_patients_df0_nm)
    
    # ***haven't worked out how to fit our model into df0 data!!!***
    1. Write a paragraph summarising the most important findings of your final model. Include the most important values from the statistical output, and a simple clinical interpretation.

    Create your response to this task here, as a mixture of embedded (knitr) R code and any resulting outputs, and explanatory or commentary text.

    Task 2 (15 marks)

    In this task, you are required to develop a Cox proportional hazards survival model using the icu_patients_df1 data set which adequately explains or predicts the length of survival indicated by the Days variable, with censoring as indicated by the Status variable. You should fit a series of models, maybe three or four, evaluating each one, before you present your final model. Your final model should not include all the predictor variables, just a small subset of them, which you have selected based on statistical significance and/or background knowledge. Aim for between five and ten predictor variables (slightly more or fewer is OK). It is perfectly acceptable to include predictor variables in your final model which are not statistically significant, as long as you justify their inclusion on medical or physiological grounds (you will not be marked down if your medical justification is not exactly correct, but do you best). You should assess each model you consider for goodness of fit and other relevant statistics, and you should assess your final model for violations of assumptions and perform other diagnostics which you think are relevant (and modify the model if indicated, or at least comment on the possible impact of what your diagnostics show). Finally, re-fit your final model to the unimputed data frame (icu_patients_df0.rds) and comment on any differences you find.

    Hints

    1. Select an initial subset of explanatory variables that you will use to predict survival. Justify your choice.
    #Survival anlaysis Data set up
    library(survival)
    library(eha)
    library(stringi)
    library(bshazard)
    ## Loading required package: splines
    ## Loading required package: Epi
    library(survminer)
    ## Loading required package: ggpubr
    #Available variables
    head(icu_patients_df1)
    ##   RecordID Length_of_stay SAPS1 SOFA Survival in_hospital_death Days Status Age
    ## 1   132539              5     6    1       NA                 0 2408  FALSE  54
    ## 2   132540              8    16    8       NA                 0 2408  FALSE  76
    ## 3   132541             19    21   11       NA                 0 2408  FALSE  44
    ## 4   132543              9     7    1      575                 0  575   TRUE  68
    ## 5   132545              4    17    2      918                 0  918   TRUE  88
    ## 6   132547              6    14   11     1637                 0 1637   TRUE  64
    ##   Albumin_diff Albumin_max Albumin_min   ALP_diff ALP_max ALP_min  ALT_diff
    ## 1    0.2186633         3.2         3.1 118.147964     214     202  80.44617
    ## 2    0.8813367         2.1         2.2 252.147964     338     348  94.44617
    ## 3    0.6813367         2.7         2.3  31.147964     127     105  45.44617
    ## 4    1.4186633         4.4         4.4   9.147964     105     105 108.44617
    ## 5    0.3813367         2.7         2.6  56.852036      39      78  96.44617
    ## 6    0.4186633         3.4         3.3   5.147964     101     101  75.44617
    ##   ALT_max ALT_min  AST_diff AST_max AST_min Bilirubin_diff Bilirubin_max
    ## 1      40      75 131.35271      38      53       1.464039           0.4
    ## 2     206      26 116.35271      53      74       1.564039           1.2
    ## 3      91      75  65.64729     235     164       1.235961           3.0
    ## 4      12      12 154.35271      15      15       1.564039           0.2
    ## 5      24      32 154.35271      15      97       1.364039           0.4
    ## 6      60      45 122.35271     162      47       1.364039           0.4
    ##   Bilirubin_min  BUN_diff BUN_max BUN_min Cholesterol_diff Cholesterol_max
    ## 1           0.3 11.527053      13      13         16.42276             154
    ## 2           0.2  8.527053      18      16         28.42276             139
    ## 3           2.8 21.527053       8       3         56.42276             111
    ## 4           0.2  4.527053      23      20         37.42276             127
    ## 5           0.9 20.472947      45      45         55.42276             104
    ## 6           0.4  9.527053      19      15         55.57724             212
    ##   Cholesterol_min Creatinine_diff Creatinine_max Creatinine_min DiasABP_diff
    ## 1             140       0.4324463            0.8            0.8           NA
    ## 2             128       0.4324463            1.2            0.8     26.54421
    ## 3             100       0.9324463            0.4            0.3           NA
    ## 4             119       0.5324463            0.9            0.7           NA
    ## 5             101       0.2324463            1.0            1.0           NA
    ## 6             212       0.3324463            1.4            0.9     20.45579
    ##   DiasABP_max DiasABP_min  FiO2_diff FiO2_max FiO2_min GCS_diff GCS_max GCS_min
    ## 1          NA          NA 0.05192012      0.5      0.5 3.755971      15      15
    ## 2          81          32 0.44807988      1.0      0.4 8.244029      15       3
    ## 3          NA          NA 0.44807988      1.0      0.5 6.244029       8       5
    ## 4          NA          NA 0.44807988      1.0      0.4 3.755971      15      14
    ## 5          NA          NA 0.15192012      0.4      0.5 3.755971      15      15
    ## 6          79          55 0.05192012      0.5      0.5 4.244029       9       7
    ##   Gender Glucose_diff Glucose_max Glucose_min HCO3_diff HCO3_max HCO3_min
    ## 1 Female     65.14446         205         205  3.227452       26       26
    ## 2   Male     34.85554         105         105  1.772548       22       21
    ## 3 Female     20.85554         141         119  3.227452       26       24
    ## 4   Male     33.85554         129         106  5.227452       28       27
    ## 5 Female     26.85554         113         113  4.772548       18       18
    ## 6   Male    124.14446         264         197  3.772548       19       19
    ##    HCT_diff HCT_max HCT_min Height   HR_diff HR_max HR_min
    ## 1  2.739871    33.7    33.5     NA 29.077891     80     58
    ## 2  6.260129    29.7    24.7  175.3  7.077891     88     80
    ## 3  4.260129    28.5    26.7     NA 30.077891    113     57
    ## 4 10.339871    41.3    36.1  180.3 30.077891     88     57
    ## 5  8.360129    30.8    22.6     NA 20.077891     94     67
    ## 6 10.639871    41.6    36.8  180.3 16.077891     91     71
    ##                         ICUType    K_diff K_max K_min Lactate_diff Lactate_max
    ## 1                  Surgical ICU 0.2647934   4.4   4.4    0.9964037         1.9
    ## 2 Cardiac Surgery Recovery Unit 0.1647934   4.3   4.3    1.4964037         2.9
    ## 3                   Medical ICU 4.4647934   8.6   3.3    1.4964037         1.9
    ## 4                   Medical ICU 0.1352066   4.2   4.0    1.5964037         1.2
    ## 5                   Medical ICU 1.8647934   6.0   3.8    0.8964037         2.0
    ## 6            Coronary Care Unit 0.9647934   5.1   3.8    1.8964037         0.9
    ##   Lactate_min MAP_diff MAP_max MAP_min   Mg_diff Mg_max Mg_min   Na_diff Na_max
    ## 1         1.8 31.23164     109      56 0.4842982    1.5    1.5 2.2066071    137
    ## 2         1.3 34.76836     100      43 1.1157018    3.1    1.9 0.2066071    139
    ## 3         1.3 53.23164     131      71 0.6842982    1.9    1.3 2.2066071    140
    ## 4         1.5 24.23164     102      72 0.1157018    2.1    2.1 1.7933929    141
    ## 5         1.9  9.76836      78      68 0.4842982    1.5    1.5 0.7933929    140
    ## 6         1.3 24.23164     102      62 0.2842982    1.7    1.7 2.2066071    141
    ##   Na_min NIDiasABP_diff NIDiasABP_max NIDiasABP_min NIMAP_diff NIMAP_max
    ## 1    137       17.49101            65            40   17.04069     92.33
    ## 2    139       19.49101            65            38   26.38069     86.33
    ## 3    137       37.50899            95            66   34.28931    110.00
    ## 4    140       23.50899            81            54   24.98931    100.70
    ## 5    140       38.50899            96            29   29.98931    105.70
    ## 6    137       31.50899            89            52   26.58931    102.30
    ##   NIMAP_min NISysABP_diff NISysABP_max NISysABP_min PaCO2_diff PaCO2_max
    ## 1     58.67      40.30125          157           96   3.335797        37
    ## 2     49.33      44.69875          129           72   7.335797        41
    ## 3     83.33      33.30125          150          111   3.335797        37
    ## 4     73.00      23.30125          140          102   9.335797        38
    ## 5     63.67      39.30125          156          119   6.335797        34
    ## 6     61.67      35.69875          129           81   5.335797        45
    ##   PaCO2_min PaO2_diff PaO2_max PaO2_min    pH_diff pH_max pH_min Platelets_diff
    ## 1        38  47.61789      186      111 0.12011376   7.49   7.43       31.23069
    ## 2        33 286.38211      445       89 0.08011376   7.45   7.34       36.23069
    ## 3        37  93.61789       65       65 0.14011376   7.51   7.51      117.76931
    ## 4        31  94.61789      148       64 0.14011376   7.51   7.47      201.23069
    ## 5        35  80.61789       78       84 0.04011376   7.38   7.41       80.76931
    ## 6        35  80.61789      101       78 0.07988624   7.40   7.29       86.23069
    ##   Platelets_max Platelets_min RespRate_diff RespRate_max RespRate_min SaO2_diff
    ## 1           221           221       7.34858           24           12  3.246079
    ## 2           226           164      16.65142           36           11  1.753921
    ## 3            84            72      13.65142           33           18  2.246079
    ## 4           391           315       7.34858           21           12  1.753921
    ## 5           109           109       6.65142           26           15  3.246079
    ## 6           276           219      27.65142           47           20  1.246079
    ##   SaO2_max SaO2_min SysABP_diff SysABP_max SysABP_min Temp_diff Temp_max
    ## 1       98       94          NA         NA         NA  1.874083     38.1
    ## 2       99       97     50.3105        135         66  2.474083     37.9
    ## 3       95       95          NA         NA         NA  2.025917     39.0
    ## 4       99       97          NA         NA         NA  1.874083     36.7
    ## 5       97       94          NA         NA         NA  1.174083     37.8
    ## 6       97       96     43.3105        152         73  1.174083     37.8
    ##   Temp_min TroponinI_diff TroponinI_max TroponinI_min TroponinT_diff
    ## 1     35.1      5.1429448           1.0           0.3      0.4785006
    ## 2     34.5     26.2570552          31.7          16.1      0.6485006
    ## 3     36.7     31.2570552          33.4          36.7      0.8814994
    ## 4     35.1      0.8570552           5.9           6.3      0.6485006
    ## 5     35.8      0.1570552           5.6           5.6      0.6085006
    ## 6     35.8      4.1429448           1.3           1.3      0.6385006
    ##   TroponinT_max TroponinT_min Urine_diff Urine_max Urine_min   WBC_diff WBC_max
    ## 1          0.58          0.19  800.78242       900        30  0.9331524    11.2
    ## 2          0.43          0.02  670.78242       770         0  4.7331524    13.1
    ## 3          1.55          1.41  310.78242       410        30  8.4331524     4.2
    ## 4          0.10          0.02  600.78242       700       100  3.3331524    11.5
    ## 5          0.06          0.37   83.21758       150        16  8.3331524     3.8
    ## 6          0.03          0.10 1100.78242      1200        40 11.8668476    24.0
    ##   WBC_min Weight_diff Weight_max Weight_min PFratio
    ## 1    11.2          NA         NA         NA     222
    ## 2     7.4    4.699878       80.6       76.0      89
    ## 3     3.7   23.999878       56.7       56.7      65
    ## 4     8.8    3.900122       84.6       84.6      64
    ## 5     3.8          NA         NA         NA     210
    ## 6    14.4   33.300122      114.0      114.0     156

    **Selecting an initial subset of explanatory variables:

    To select a subset of explanatory variables our group of investigators will examine the SAPS1 score and the SOFA score included in the dataset in more detail to ascertain the variables that might be logically associated with increased mortality and poor survival. We will also assess the APACHE score which is commonly used in ICU risk predcition models.

    SAPS1 - Simplified Acute Physiology Score is a measure of the severity of disease for patients admitted to ICU. The following measures increases the SAPS1 score:

    • Advanced Age
    • Low and high Heart Rate
    • Low and high Systolic Blood Pressure
    • High Temperature
    • Low Glasgow Coma Scale (However it is most meaningful to use the highest GCS score available for prognostication)
    • Mechanical Ventilation or CPAP
    • High PaO2/ FiO2 ratio (It is likely that highes FiO2 is administered during lowest PaO2)
    • Low Urine Output
    • High Blood Urea Nitrogen
    • Low or High Sodium
    • Low or high Potassium
    • Low Bicarbonate
    • High Bilirubin
    • Low or High White Blood Cell
    • Chronic diseases
    • Type of admission (ie ICU Type)

    SOFA - sequential organ failure assessment is a predictor of ICU mortality. The following measures increase the SOFA score: Elevated PaO2/ FiO2 ratio- * Reduced GCS - Nervous system * Reduced MAP - Cardiovascular system * Administration of vasopressors - Cardiovascular system * High Bilirubin - Liver * Low Platelets - Coagulation * High Creatinine - Kidneys * Low Urine - Kidneys

    *The APACHE score is commonly used validated risk score for ICU risk prediction. The variables that increase the APACHE score include:

    • Advanced Age

    • High or Low Temperature

    • High or Low MAP

    • High or Low HR

    • High or Low Respiratory Rate

    • High PaO2/FiO2 ratio

    • High or Low pH

    • High or Low Na

    • High or Low K

    • High Creatinine

    • High or low HCT

    • High or Low WBC

    • For our analysis, we will include variables that will increase SOFA, SAPS or APACHE scores. eg: increased BUN and reduced HCO3 will increase the SAPS score, therfore we will include BUN max(but not BUN_min and BUN_diff) and HCO3_min (but not HCO3_max and HCO3_diff). Where both extremes of a variable will increase the risk score, both min and max variables will be included.

    • Other factors known to be associated with morbidity/ mortality not included in risk scores:

      • Height/ weight - Body composition/ BMI is associated with mortality and survival
      • Gender - Male gender associated with worse outcomes
      • Glucose - high and low Glucose levels are associated with pathology
      • Troponin T and I - high troponin results(cardiac biomarkers) associated with morbidity and mortality
      • Lactate - elevated lactate is associated with poor organ perfusion and ICU morbidity/ mortality
      • Albumin - reduced albumin is associated with poor clinical outcomes

    BELOW IS A LIST OF THE VARIABLES TO BE INCLUDED: DEMOGRAPHIC VARAIBLES: * Age * Gender * ICU Type * Height * Weight_max

    CLINICAL VARIABLES: * Albumin_min * Bilirubin_max * BUN_max * Creatinine_max
    * GCS_min * Glucose_min and Glucose_max * HCO3_min * HR_min and HR_max * K_min K_max * Lactate_max * MAP_min
    * Na_min and Na_max * NISysABP_min and NISysABP_max * Platelets_min * FiO2_max and PaO2_min - included as PFratio: PaO2_min/ FiO2_max * pH_min and pH_max * RespRate_min and RespRate_max * Temp_min and Temp_max * TroponinI_max * TroponinT_max * Urine_min * WBC_min and WBC_max

    1. Conduct basic exploratory data analysis on your variables of choice.
    # Outcome variables
    unique_icu = unique(subset(icu_patients_df1, select = c(RecordID)))
    dim(unique_icu) # There are 2061 unique individuals
    ## [1] 2061    1
    table(icu_patients_df1$Status) #773 censored out of 2061 observations
    ## 
    ## FALSE  TRUE 
    ##  1288   773
    # Plot KM survival curve (non-parametric)
    ICU.fit <- survfit( Surv(Days, Status) ~ 1, data = icu_patients_df1) 
    print(ICU.fit, print.rmean = TRUE)
    ## Call: survfit(formula = Surv(Days, Status) ~ 1, data = icu_patients_df1)
    ## 
    ##          n     events     *rmean *se(rmean)     median    0.95LCL    0.95UCL 
    ##     2061.0      773.0     1633.5       23.1         NA         NA         NA 
    ##     * restricted mean with upper limit =  2408
    summary(ICU.fit)
    ## Call: survfit(formula = Surv(Days, Status) ~ 1, data = icu_patients_df1)
    ## 
    ##  time n.risk n.event survival  std.err lower 95% CI upper 95% CI
    ##     0   2061       2    0.999 0.000686        0.998        1.000
    ##     1   2059      16    0.991 0.002050        0.987        0.995
    ##     2   2043      26    0.979 0.003184        0.972        0.985
    ##     3   2017      30    0.964 0.004098        0.956        0.972
    ##     4   1987      20    0.954 0.004596        0.945        0.963
    ##     5   1967      22    0.944 0.005077        0.934        0.954
    ##     6   1945      13    0.937 0.005336        0.927        0.948
    ##     7   1932      18    0.929 0.005669        0.918        0.940
    ##     8   1914      11    0.923 0.005860        0.912        0.935
    ##     9   1903      24    0.912 0.006250        0.900        0.924
    ##    10   1879      16    0.904 0.006491        0.891        0.917
    ##    11   1863      13    0.898 0.006677        0.885        0.911
    ##    12   1850      13    0.891 0.006856        0.878        0.905
    ##    13   1837       8    0.887 0.006962        0.874        0.901
    ##    14   1829       6    0.885 0.007040        0.871        0.898
    ##    15   1823      11    0.879 0.007179        0.865        0.893
    ##    16   1812       9    0.875 0.007289        0.861        0.889
    ##    17   1803       8    0.871 0.007385        0.857        0.886
    ##    18   1795       4    0.869 0.007432        0.855        0.884
    ##    19   1791       7    0.866 0.007513        0.851        0.880
    ##    20   1784       5    0.863 0.007570        0.848        0.878
    ##    21   1779       8    0.859 0.007659        0.844        0.874
    ##    22   1771       3    0.858 0.007692        0.843        0.873
    ##    23   1768       3    0.856 0.007725        0.841        0.872
    ##    24   1765       3    0.855 0.007757        0.840        0.870
    ##    25   1762       4    0.853 0.007800        0.838        0.868
    ##    26   1758       3    0.852 0.007832        0.836        0.867
    ##    27   1755       3    0.850 0.007864        0.835        0.866
    ##    28   1752       3    0.849 0.007895        0.833        0.864
    ##    29   1749       2    0.848 0.007916        0.832        0.863
    ##    30   1747       2    0.847 0.007936        0.831        0.862
    ##    31   1745       5    0.844 0.007987        0.829        0.860
    ##    32   1740       1    0.844 0.007998        0.828        0.860
    ##    33   1739       2    0.843 0.008018        0.827        0.859
    ##    34   1737       1    0.842 0.008028        0.827        0.858
    ##    35   1736       1    0.842 0.008038        0.826        0.858
    ##    36   1735       3    0.840 0.008068        0.825        0.856
    ##    37   1732       1    0.840 0.008078        0.824        0.856
    ##    38   1731       4    0.838 0.008117        0.822        0.854
    ##    39   1727       3    0.836 0.008146        0.821        0.853
    ##    40   1724       1    0.836 0.008156        0.820        0.852
    ##    41   1723       3    0.835 0.008185        0.819        0.851
    ##    42   1720       1    0.834 0.008195        0.818        0.850
    ##    45   1719       2    0.833 0.008214        0.817        0.849
    ##    46   1717       3    0.832 0.008242        0.816        0.848
    ##    47   1714       2    0.831 0.008261        0.815        0.847
    ##    48   1712       3    0.829 0.008289        0.813        0.846
    ##    49   1709       1    0.829 0.008299        0.813        0.845
    ##    50   1708       3    0.827 0.008327        0.811        0.844
    ##    51   1705       1    0.827 0.008336        0.811        0.843
    ##    52   1704       1    0.826 0.008345        0.810        0.843
    ##    53   1703       1    0.826 0.008354        0.810        0.842
    ##    54   1702       1    0.825 0.008363        0.809        0.842
    ##    55   1701       2    0.824 0.008382        0.808        0.841
    ##    56   1699       3    0.823 0.008409        0.807        0.840
    ##    57   1696       1    0.822 0.008418        0.806        0.839
    ##    58   1695       2    0.821 0.008436        0.805        0.838
    ##    60   1693       5    0.819 0.008481        0.803        0.836
    ##    61   1688       3    0.818 0.008507        0.801        0.834
    ##    62   1685       1    0.817 0.008516        0.801        0.834
    ##    63   1684       1    0.817 0.008525        0.800        0.833
    ##    64   1683       1    0.816 0.008533        0.800        0.833
    ##    65   1682       5    0.814 0.008577        0.797        0.831
    ##    66   1677       2    0.813 0.008594        0.796        0.830
    ##    68   1675       2    0.812 0.008611        0.795        0.829
    ##    69   1673       2    0.811 0.008628        0.794        0.828
    ##    70   1671       1    0.810 0.008636        0.794        0.827
    ##    73   1670       3    0.809 0.008662        0.792        0.826
    ##    76   1667       1    0.808 0.008670        0.792        0.826
    ##    78   1666       1    0.808 0.008678        0.791        0.825
    ##    80   1665       1    0.807 0.008687        0.791        0.825
    ##    81   1664       1    0.807 0.008695        0.790        0.824
    ##    82   1663       1    0.806 0.008703        0.790        0.824
    ##    84   1662       1    0.806 0.008712        0.789        0.823
    ##    85   1661       1    0.805 0.008720        0.789        0.823
    ##    86   1660       3    0.804 0.008744        0.787        0.821
    ##    87   1657       1    0.803 0.008753        0.787        0.821
    ##    88   1656       1    0.803 0.008761        0.786        0.820
    ##    90   1655       1    0.803 0.008769        0.786        0.820
    ##    93   1654       1    0.802 0.008777        0.785        0.819
    ##    95   1653       2    0.801 0.008793        0.784        0.818
    ##    96   1651       1    0.801 0.008801        0.784        0.818
    ##    97   1650       1    0.800 0.008809        0.783        0.818
    ##    98   1649       1    0.800 0.008817        0.783        0.817
    ##    99   1648       1    0.799 0.008825        0.782        0.817
    ##   102   1647       1    0.799 0.008833        0.782        0.816
    ##   103   1646       2    0.798 0.008849        0.781        0.815
    ##   104   1644       3    0.796 0.008873        0.779        0.814
    ##   105   1641       3    0.795 0.008896        0.778        0.812
    ##   109   1638       2    0.794 0.008912        0.777        0.811
    ##   111   1636       1    0.793 0.008920        0.776        0.811
    ##   112   1635       3    0.792 0.008943        0.775        0.810
    ##   114   1632       1    0.791 0.008950        0.774        0.809
    ##   116   1631       1    0.791 0.008958        0.774        0.809
    ##   120   1630       1    0.790 0.008966        0.773        0.808
    ##   126   1629       1    0.790 0.008973        0.773        0.808
    ##   127   1628       1    0.789 0.008981        0.772        0.807
    ##   128   1627       3    0.788 0.009004        0.771        0.806
    ##   129   1624       1    0.787 0.009011        0.770        0.805
    ##   130   1623       1    0.787 0.009019        0.770        0.805
    ##   132   1622       2    0.786 0.009034        0.769        0.804
    ##   133   1620       1    0.786 0.009041        0.768        0.803
    ##   134   1619       1    0.785 0.009048        0.768        0.803
    ##   135   1618       1    0.785 0.009056        0.767        0.803
    ##   138   1617       1    0.784 0.009063        0.767        0.802
    ##   140   1616       1    0.784 0.009071        0.766        0.802
    ##   141   1615       2    0.783 0.009085        0.765        0.801
    ##   142   1613       1    0.782 0.009093        0.765        0.800
    ##   143   1612       1    0.782 0.009100        0.764        0.800
    ##   144   1611       1    0.781 0.009107        0.764        0.799
    ##   145   1610       2    0.780 0.009122        0.763        0.798
    ##   149   1608       2    0.779 0.009136        0.762        0.797
    ##   151   1606       1    0.779 0.009143        0.761        0.797
    ##   157   1605       1    0.778 0.009150        0.761        0.796
    ##   159   1604       1    0.778 0.009158        0.760        0.796
    ##   162   1603       2    0.777 0.009172        0.759        0.795
    ##   163   1601       1    0.776 0.009179        0.759        0.795
    ##   166   1600       2    0.775 0.009193        0.758        0.794
    ##   168   1598       1    0.775 0.009200        0.757        0.793
    ##   173   1597       1    0.774 0.009207        0.757        0.793
    ##   174   1596       1    0.774 0.009214        0.756        0.792
    ##   175   1595       1    0.773 0.009221        0.756        0.792
    ##   177   1594       1    0.773 0.009228        0.755        0.791
    ##   179   1593       3    0.771 0.009249        0.754        0.790
    ##   181   1590       2    0.770 0.009263        0.753        0.789
    ##   183   1588       3    0.769 0.009283        0.751        0.787
    ##   184   1585       1    0.769 0.009290        0.751        0.787
    ##   185   1584       1    0.768 0.009297        0.750        0.787
    ##   186   1583       1    0.768 0.009304        0.750        0.786
    ##   187   1582       1    0.767 0.009310        0.749        0.786
    ##   193   1581       1    0.767 0.009317        0.749        0.785
    ##   195   1580       2    0.766 0.009331        0.748        0.784
    ##   197   1578       3    0.764 0.009351        0.746        0.783
    ##   198   1575       1    0.764 0.009357        0.746        0.782
    ##   202   1574       1    0.763 0.009364        0.745        0.782
    ##   203   1573       2    0.762 0.009377        0.744        0.781
    ##   204   1571       1    0.762 0.009384        0.744        0.780
    ##   206   1570       2    0.761 0.009397        0.743        0.779
    ##   208   1568       1    0.760 0.009403        0.742        0.779
    ##   214   1567       2    0.759 0.009416        0.741        0.778
    ##   217   1565       1    0.759 0.009423        0.741        0.778
    ##   219   1564       1    0.758 0.009429        0.740        0.777
    ##   223   1563       1    0.758 0.009436        0.740        0.777
    ##   226   1562       1    0.757 0.009442        0.739        0.776
    ##   227   1561       1    0.757 0.009449        0.739        0.776
    ##   232   1560       2    0.756 0.009461        0.738        0.775
    ##   234   1558       1    0.755 0.009468        0.737        0.774
    ##   236   1557       1    0.755 0.009474        0.737        0.774
    ##   237   1556       3    0.754 0.009493        0.735        0.772
    ##   238   1553       1    0.753 0.009499        0.735        0.772
    ##   245   1552       1    0.753 0.009505        0.734        0.771
    ##   247   1551       1    0.752 0.009512        0.734        0.771
    ##   248   1550       1    0.752 0.009518        0.733        0.770
    ##   252   1549       1    0.751 0.009524        0.733        0.770
    ##   254   1548       1    0.751 0.009530        0.732        0.770
    ##   261   1547       1    0.750 0.009537        0.732        0.769
    ##   265   1546       1    0.750 0.009543        0.731        0.769
    ##   267   1545       1    0.749 0.009549        0.731        0.768
    ##   269   1544       6    0.746 0.009585        0.728        0.765
    ##   277   1538       1    0.746 0.009591        0.727        0.765
    ##   280   1537       1    0.745 0.009598        0.727        0.764
    ##   282   1536       1    0.745 0.009604        0.726        0.764
    ##   284   1535       1    0.744 0.009610        0.726        0.763
    ##   286   1534       2    0.743 0.009621        0.725        0.762
    ##   293   1532       1    0.743 0.009627        0.724        0.762
    ##   294   1531       1    0.742 0.009633        0.724        0.761
    ##   296   1530       2    0.741 0.009645        0.723        0.761
    ##   298   1528       2    0.740 0.009657        0.722        0.760
    ##   301   1526       2    0.739 0.009669        0.721        0.759
    ##   304   1524       1    0.739 0.009674        0.720        0.758
    ##   307   1523       1    0.738 0.009680        0.720        0.758
    ##   311   1522       1    0.738 0.009686        0.719        0.757
    ##   317   1521       1    0.738 0.009692        0.719        0.757
    ##   321   1520       1    0.737 0.009698        0.718        0.756
    ##   322   1519       1    0.737 0.009703        0.718        0.756
    ##   323   1518       1    0.736 0.009709        0.717        0.755
    ##   331   1517       1    0.736 0.009715        0.717        0.755
    ##   335   1516       2    0.735 0.009726        0.716        0.754
    ##   336   1514       1    0.734 0.009732        0.715        0.753
    ##   338   1513       1    0.734 0.009737        0.715        0.753
    ##   343   1512       1    0.733 0.009743        0.714        0.752
    ##   344   1511       1    0.733 0.009749        0.714        0.752
    ##   345   1510       1    0.732 0.009754        0.713        0.752
    ##   346   1509       1    0.732 0.009760        0.713        0.751
    ##   347   1508       1    0.731 0.009766        0.712        0.751
    ##   349   1507       1    0.731 0.009771        0.712        0.750
    ##   350   1506       1    0.730 0.009777        0.711        0.750
    ##   352   1505       1    0.730 0.009782        0.711        0.749
    ##   354   1504       1    0.729 0.009788        0.710        0.749
    ##   356   1503       1    0.729 0.009793        0.710        0.748
    ##   363   1502       1    0.728 0.009799        0.709        0.748
    ##   365   1501       1    0.728 0.009804        0.709        0.747
    ##   370   1500       2    0.727 0.009815        0.708        0.746
    ##   376   1498       1    0.726 0.009820        0.707        0.746
    ##   381   1497       1    0.726 0.009826        0.707        0.745
    ##   382   1496       1    0.725 0.009831        0.706        0.745
    ##   386   1495       1    0.725 0.009837        0.706        0.744
    ##   390   1494       2    0.724 0.009847        0.705        0.743
    ##   391   1492       1    0.723 0.009853        0.704        0.743
    ##   395   1491       1    0.723 0.009858        0.704        0.743
    ##   400   1490       2    0.722 0.009869        0.703        0.742
    ##   402   1488       1    0.721 0.009874        0.702        0.741
    ##   404   1487       1    0.721 0.009879        0.702        0.741
    ##   412   1486       2    0.720 0.009890        0.701        0.740
    ##   413   1484       1    0.720 0.009895        0.700        0.739
    ##   417   1483       1    0.719 0.009900        0.700        0.739
    ##   420   1482       1    0.719 0.009905        0.699        0.738
    ##   427   1481       1    0.718 0.009911        0.699        0.738
    ##   435   1480       1    0.718 0.009916        0.698        0.737
    ##   441   1479       1    0.717 0.009921        0.698        0.737
    ##   447   1478       1    0.717 0.009926        0.697        0.736
    ##   449   1477       1    0.716 0.009931        0.697        0.736
    ##   458   1476       1    0.716 0.009936        0.696        0.735
    ##   459   1475       1    0.715 0.009941        0.696        0.735
    ##   463   1474       2    0.714 0.009952        0.695        0.734
    ##   473   1472       1    0.714 0.009957        0.694        0.734
    ##   490   1471       1    0.713 0.009962        0.694        0.733
    ##   494   1470       2    0.712 0.009972        0.693        0.732
    ##   496   1468       1    0.712 0.009977        0.693        0.732
    ##   506   1467       1    0.711 0.009982        0.692        0.731
    ##   514   1466       1    0.711 0.009987        0.692        0.731
    ##   515   1465       1    0.710 0.009992        0.691        0.730
    ##   526   1464       1    0.710 0.009997        0.691        0.730
    ##   527   1463       2    0.709 0.010007        0.690        0.729
    ##   535   1461       1    0.708 0.010011        0.689        0.728
    ##   541   1460       1    0.708 0.010016        0.689        0.728
    ##   545   1459       1    0.707 0.010021        0.688        0.727
    ##   548   1458       1    0.707 0.010026        0.688        0.727
    ##   558   1457       1    0.706 0.010031        0.687        0.726
    ##   559   1456       1    0.706 0.010036        0.687        0.726
    ##   561   1455       1    0.705 0.010041        0.686        0.725
    ##   563   1454       1    0.705 0.010045        0.686        0.725
    ##   575   1453       1    0.705 0.010050        0.685        0.724
    ##   579   1452       1    0.704 0.010055        0.685        0.724
    ##   582   1451       1    0.704 0.010060        0.684        0.724
    ##   589   1450       1    0.703 0.010065        0.684        0.723
    ##   593   1449       1    0.703 0.010069        0.683        0.723
    ##   607   1448       1    0.702 0.010074        0.683        0.722
    ##   609   1447       1    0.702 0.010079        0.682        0.722
    ##   610   1446       1    0.701 0.010083        0.682        0.721
    ##   611   1445       2    0.700 0.010093        0.681        0.720
    ##   615   1443       1    0.700 0.010097        0.680        0.720
    ##   623   1442       2    0.699 0.010107        0.679        0.719
    ##   628   1440       1    0.698 0.010111        0.679        0.718
    ##   647   1439       1    0.698 0.010116        0.678        0.718
    ##   653   1438       1    0.697 0.010121        0.678        0.717
    ##   682   1437       1    0.697 0.010125        0.677        0.717
    ##   683   1436       1    0.696 0.010130        0.677        0.716
    ##   693   1435       1    0.696 0.010134        0.676        0.716
    ##   700   1434       1    0.695 0.010139        0.676        0.715
    ##   701   1433       1    0.695 0.010143        0.675        0.715
    ##   713   1432       1    0.694 0.010148        0.675        0.715
    ##   719   1431       1    0.694 0.010152        0.674        0.714
    ##   726   1430       1    0.693 0.010157        0.674        0.714
    ##   730   1429       1    0.693 0.010161        0.673        0.713
    ##   731   1428       1    0.692 0.010166        0.673        0.713
    ##   740   1427       2    0.691 0.010175        0.672        0.712
    ##   743   1425       1    0.691 0.010179        0.671        0.711
    ##   775   1424       1    0.690 0.010183        0.671        0.711
    ##   776   1423       1    0.690 0.010188        0.670        0.710
    ##   778   1422       1    0.689 0.010192        0.670        0.710
    ##   795   1421       1    0.689 0.010197        0.669        0.709
    ##   808   1420       1    0.689 0.010201        0.669        0.709
    ##   811   1419       1    0.688 0.010205        0.668        0.708
    ##   814   1418       1    0.688 0.010210        0.668        0.708
    ##   820   1417       1    0.687 0.010214        0.667        0.707
    ##   833   1416       2    0.686 0.010223        0.666        0.706
    ##   839   1414       1    0.686 0.010227        0.666        0.706
    ##   844   1413       1    0.685 0.010231        0.665        0.705
    ##   847   1412       2    0.684 0.010240        0.664        0.705
    ##   850   1410       1    0.684 0.010244        0.664        0.704
    ##   858   1409       1    0.683 0.010248        0.663        0.704
    ##   860   1408       1    0.683 0.010252        0.663        0.703
    ##   878   1407       1    0.682 0.010256        0.662        0.703
    ##   895   1406       1    0.682 0.010261        0.662        0.702
    ##   917   1405       1    0.681 0.010265        0.661        0.702
    ##   918   1404       2    0.680 0.010273        0.660        0.701
    ##   926   1402       2    0.679 0.010281        0.659        0.700
    ##   931   1400       1    0.679 0.010285        0.659        0.699
    ##   933   1399       1    0.678 0.010289        0.658        0.699
    ##   946   1398       1    0.678 0.010294        0.658        0.698
    ##   958   1397       2    0.677 0.010302        0.657        0.697
    ##   965   1395       1    0.676 0.010306        0.656        0.697
    ##   972   1394       1    0.676 0.010310        0.656        0.696
    ##   975   1393       1    0.675 0.010314        0.655        0.696
    ##   976   1392       1    0.675 0.010318        0.655        0.695
    ##   977   1391       1    0.674 0.010322        0.655        0.695
    ##   981   1390       1    0.674 0.010326        0.654        0.694
    ##   988   1389       1    0.673 0.010330        0.654        0.694
    ##   994   1388       1    0.673 0.010334        0.653        0.694
    ##  1001   1387       1    0.672 0.010338        0.653        0.693
    ##  1011   1386       1    0.672 0.010341        0.652        0.693
    ##  1012   1385       1    0.672 0.010345        0.652        0.692
    ##  1018   1384       1    0.671 0.010349        0.651        0.692
    ##  1039   1383       1    0.671 0.010353        0.651        0.691
    ##  1045   1382       1    0.670 0.010357        0.650        0.691
    ##  1046   1381       2    0.669 0.010365        0.649        0.690
    ##  1061   1379       1    0.669 0.010369        0.649        0.689
    ##  1068   1378       1    0.668 0.010372        0.648        0.689
    ##  1079   1377       1    0.668 0.010376        0.648        0.688
    ##  1082   1376       1    0.667 0.010380        0.647        0.688
    ##  1094   1375       1    0.667 0.010384        0.647        0.687
    ##  1096   1374       1    0.666 0.010388        0.646        0.687
    ##  1099   1373       1    0.666 0.010391        0.646        0.686
    ##  1100   1372       1    0.665 0.010395        0.645        0.686
    ##  1101   1371       1    0.665 0.010399        0.645        0.685
    ##  1106   1370       1    0.664 0.010403        0.644        0.685
    ##  1139   1369       1    0.664 0.010406        0.644        0.684
    ##  1162   1368       1    0.663 0.010410        0.643        0.684
    ##  1167   1367       1    0.663 0.010414        0.643        0.684
    ##  1171   1366       1    0.662 0.010417        0.642        0.683
    ##  1181   1365       1    0.662 0.010421        0.642        0.683
    ##  1216   1364       1    0.661 0.010425        0.641        0.682
    ##  1226   1363       1    0.661 0.010428        0.641        0.682
    ##  1233   1362       1    0.660 0.010432        0.640        0.681
    ##  1235   1361       1    0.660 0.010435        0.640        0.681
    ##  1252   1360       1    0.659 0.010439        0.639        0.680
    ##  1267   1359       1    0.659 0.010443        0.639        0.680
    ##  1269   1358       1    0.658 0.010446        0.638        0.679
    ##  1289   1357       1    0.658 0.010450        0.638        0.679
    ##  1318   1356       2    0.657 0.010457        0.637        0.678
    ##  1321   1354       1    0.656 0.010460        0.636        0.677
    ##  1326   1353       1    0.656 0.010464        0.636        0.677
    ##  1344   1352       1    0.656 0.010467        0.635        0.676
    ##  1353   1351       1    0.655 0.010471        0.635        0.676
    ##  1356   1350       1    0.655 0.010474        0.634        0.675
    ##  1359   1349       1    0.654 0.010478        0.634        0.675
    ##  1367   1348       1    0.654 0.010481        0.633        0.674
    ##  1408   1347       1    0.653 0.010485        0.633        0.674
    ##  1413   1346       1    0.653 0.010488        0.632        0.673
    ##  1415   1345       1    0.652 0.010492        0.632        0.673
    ##  1419   1344       1    0.652 0.010495        0.631        0.673
    ##  1422   1343       1    0.651 0.010498        0.631        0.672
    ##  1438   1342       1    0.651 0.010502        0.630        0.672
    ##  1444   1341       1    0.650 0.010505        0.630        0.671
    ##  1451   1340       1    0.650 0.010509        0.629        0.671
    ##  1459   1339       1    0.649 0.010512        0.629        0.670
    ##  1473   1338       1    0.649 0.010515        0.628        0.670
    ##  1482   1337       1    0.648 0.010519        0.628        0.669
    ##  1486   1336       1    0.648 0.010522        0.627        0.669
    ##  1488   1335       1    0.647 0.010525        0.627        0.668
    ##  1497   1334       1    0.647 0.010528        0.626        0.668
    ##  1537   1333       1    0.646 0.010532        0.626        0.667
    ##  1538   1332       1    0.646 0.010535        0.625        0.667
    ##  1548   1331       1    0.645 0.010538        0.625        0.666
    ##  1557   1330       1    0.645 0.010541        0.624        0.666
    ##  1562   1329       1    0.644 0.010545        0.624        0.665
    ##  1571   1328       1    0.644 0.010548        0.624        0.665
    ##  1590   1327       1    0.643 0.010551        0.623        0.664
    ##  1599   1326       1    0.643 0.010554        0.623        0.664
    ##  1601   1325       1    0.642 0.010557        0.622        0.663
    ##  1604   1324       1    0.642 0.010561        0.622        0.663
    ##  1637   1323       1    0.641 0.010564        0.621        0.662
    ##  1641   1322       1    0.641 0.010567        0.621        0.662
    ##  1670   1321       1    0.640 0.010570        0.620        0.662
    ##  1672   1320       1    0.640 0.010573        0.620        0.661
    ##  1692   1319       1    0.639 0.010576        0.619        0.661
    ##  1711   1318       1    0.639 0.010579        0.619        0.660
    ##  1718   1317       1    0.639 0.010583        0.618        0.660
    ##  1751   1316       1    0.638 0.010586        0.618        0.659
    ##  1758   1315       1    0.638 0.010589        0.617        0.659
    ##  1776   1314       1    0.637 0.010592        0.617        0.658
    ##  1780   1313       1    0.637 0.010595        0.616        0.658
    ##  1853   1312       1    0.636 0.010598        0.616        0.657
    ##  1858   1311       1    0.636 0.010601        0.615        0.657
    ##  1873   1310       1    0.635 0.010604        0.615        0.656
    ##  1889   1309       1    0.635 0.010607        0.614        0.656
    ##  1955   1308       1    0.634 0.010610        0.614        0.655
    ##  1967   1307       1    0.634 0.010613        0.613        0.655
    ##  1972   1306       1    0.633 0.010616        0.613        0.654
    ##  1988   1305       1    0.633 0.010619        0.612        0.654
    ##  2009   1304       1    0.632 0.010622        0.612        0.653
    ##  2011   1303       1    0.632 0.010625        0.611        0.653
    ##  2013   1302       1    0.631 0.010627        0.611        0.652
    ##  2014   1301       1    0.631 0.010630        0.610        0.652
    ##  2051   1300       1    0.630 0.010633        0.610        0.651
    ##  2053   1299       1    0.630 0.010636        0.609        0.651
    ##  2077   1298       1    0.629 0.010639        0.609        0.651
    ##  2099   1297       1    0.629 0.010642        0.608        0.650
    ##  2140   1296       1    0.628 0.010645        0.608        0.650
    ##  2141   1295       1    0.628 0.010648        0.607        0.649
    ##  2188   1294       1    0.627 0.010650        0.607        0.649
    ##  2190   1293       1    0.627 0.010653        0.606        0.648
    ##  2192   1292       1    0.626 0.010656        0.606        0.648
    ##  2333   1291       1    0.626 0.010659        0.605        0.647
    ##  2350   1290       1    0.625 0.010661        0.605        0.647
    ##  2408   1289       1    0.625 0.010664        0.604        0.646
    plot(ICU.fit, main = 'Kaplan-Meier estimate of survival function', xlab = 'Length of survival (in days)')

    # plotting Nelson-Aalen estimate (non-parametric)
    plot(ICU.fit, fun="cumhaz", main = "Nelson-Aalen estimate of cumulative hazard function", xlab = 'Length of survival (in days)')

    There were 773 deaths (out of 2061 participants) during follow-up.The median follow-up time cannot be determined as the survival rate has not yet dropped to 50% survival at the end of the available data. The cumulative hazard rate (as shown in the Nelson Aalen plot) reaches 47% by the end of the available data.

    # Display frequencies for categorical explanatory variables
    table(icu_patients_df1$Gender)
    ## 
    ## Female   Male 
    ##    913   1148
    table(icu_patients_df1$ICUType)
    ## 
    ##            Coronary Care Unit Cardiac Surgery Recovery Unit 
    ##                           297                           448 
    ##                   Medical ICU                  Surgical ICU 
    ##                           788                           528
    # Display counts, histograms, median and IQRs for continuous explanatory variables
    
    #################################################################################
    ### CODE COPIED TO TASK 1
    # Create PFratio variable:
    # icu_patients_df1$PFratio<-icu_patients_df1$PaO2_min/icu_patients_df1$FiO2_max
    ### CODE COPIED TO TASK 1
    #################################################################################
    
    # Write a function for continuous variable EDA output
    cont_eda <- function(variable){
        print(paste(variable,'EDA:'))
      
        na_rm <- na.omit(icu_patients_df1[,variable])
        print(paste('Number of non-missing values:',length(na_rm))) # number of non-missing values
        print(paste('Number of missing values:',sum(is.na(icu_patients_df1[,variable])))) # number of missing values
      
        print(quantile(icu_patients_df1[,variable], na.rm=TRUE))
        hist(icu_patients_df1[,variable], breaks=20, xlab=variable, main=paste('Histogram of',variable))
    }
    
    #################################################################################
    ### CODE COPIED TO TASK 1
    # Loop through the continuous variables from the chosen list of variables to explore and pass them to the EDA function
    # cont_vars <- c('Age', 'Height', 'Weight_max', 'Albumin_min', 'Bilirubin_max', 
    #                'BUN_max', 'Creatinine_max', 'GCS_min', 'Glucose_min', 
    #                'Glucose_max', 'HCO3_min', 'HR_min', 'HR_max', 'K_min', 'K_max', 
    #                'Lactate_max', 'MAP_min', 'Na_min', 'Na_max', 'NISysABP_min', 
    #                'NISysABP_max', 'Platelets_min', 'PFratio', 'pH_min', 'pH_max', 
    #                'RespRate_min', 'RespRate_max', 'Temp_min', 'Temp_max', 
    #                'TroponinI_max', 'TroponinT_max', 'Urine_min', 'WBC_min', 'WBC_max')
    ### CODE COPIED TO TASK 1
    #################################################################################
    
    par(mfrow=c(12,3)) # set the layout of the histograms in 12 row x 3 column grid
    for(i in 1:length(cont_vars)){
      cont_eda(cont_vars[i])
    }
    ## [1] "Age EDA:"
    ## [1] "Number of non-missing values: 2061"
    ## [1] "Number of missing values: 0"
    ##   0%  25%  50%  75% 100% 
    ##   16   52   67   78   90
    ## [1] "Height EDA:"
    ## [1] "Number of non-missing values: 1069"
    ## [1] "Number of missing values: 992"
    ##    0%   25%   50%   75%  100% 
    ##  13.0 162.6 170.2 177.8 426.7
    ## [1] "Weight_max EDA:"
    ## [1] "Number of non-missing values: 1915"
    ## [1] "Number of missing values: 146"
    ##     0%    25%    50%    75%   100% 
    ##  34.60  66.00  80.00  94.55 230.00
    ## [1] "Albumin_min EDA:"
    ## [1] "Number of non-missing values: 2061"
    ## [1] "Number of missing values: 0"
    ##   0%  25%  50%  75% 100% 
    ##  1.1  2.6  3.0  3.5  5.3
    ## [1] "Bilirubin_max EDA:"
    ## [1] "Number of non-missing values: 2061"
    ## [1] "Number of missing values: 0"
    ##   0%  25%  50%  75% 100% 
    ##  0.1  0.4  0.7  1.3 45.9
    ## [1] "BUN_max EDA:"
    ## [1] "Number of non-missing values: 2061"
    ## [1] "Number of missing values: 0"
    ##   0%  25%  50%  75% 100% 
    ##    3   14   20   33  197
    ## [1] "Creatinine_max EDA:"
    ## [1] "Number of non-missing values: 2061"
    ## [1] "Number of missing values: 0"
    ##   0%  25%  50%  75% 100% 
    ##  0.2  0.8  1.0  1.5 22.0
    ## [1] "GCS_min EDA:"
    ## [1] "Number of non-missing values: 2061"
    ## [1] "Number of missing values: 0"
    ##   0%  25%  50%  75% 100% 
    ##    3    3    8   14   15
    ## [1] "Glucose_min EDA:"
    ## [1] "Number of non-missing values: 2061"
    ## [1] "Number of missing values: 0"
    ##   0%  25%  50%  75% 100% 
    ##   24   98  117  141  632
    ## [1] "Glucose_max EDA:"
    ## [1] "Number of non-missing values: 2061"
    ## [1] "Number of missing values: 0"
    ##   0%  25%  50%  75% 100% 
    ##   39  117  141  180 1143
    ## [1] "HCO3_min EDA:"
    ## [1] "Number of non-missing values: 2061"
    ## [1] "Number of missing values: 0"
    ##   0%  25%  50%  75% 100% 
    ##    5   20   23   25   44
    ## [1] "HR_min EDA:"
    ## [1] "Number of non-missing values: 2061"
    ## [1] "Number of missing values: 0"
    ##   0%  25%  50%  75% 100% 
    ##    0   61   71   81  126
    ## [1] "HR_max EDA:"
    ## [1] "Number of non-missing values: 2061"
    ## [1] "Number of missing values: 0"
    ##   0%  25%  50%  75% 100% 
    ##   44   91  104  119  300
    ## [1] "K_min EDA:"
    ## [1] "Number of non-missing values: 2061"
    ## [1] "Number of missing values: 0"
    ##   0%  25%  50%  75% 100% 
    ##  1.8  3.5  3.9  4.3  6.9
    ## [1] "K_max EDA:"
    ## [1] "Number of non-missing values: 2061"
    ## [1] "Number of missing values: 0"
    ##   0%  25%  50%  75% 100% 
    ##  2.5  4.0  4.3  4.7 22.9
    ## [1] "Lactate_max EDA:"
    ## [1] "Number of non-missing values: 2061"
    ## [1] "Number of missing values: 0"
    ##   0%  25%  50%  75% 100% 
    ##  0.4  1.5  2.2  3.2 29.3
    ## [1] "MAP_min EDA:"
    ## [1] "Number of non-missing values: 2061"
    ## [1] "Number of missing values: 0"
    ##   0%  25%  50%  75% 100% 
    ##    1   55   61   70  265
    ## [1] "Na_min EDA:"
    ## [1] "Number of non-missing values: 2061"
    ## [1] "Number of missing values: 0"
    ##   0%  25%  50%  75% 100% 
    ##   98  136  138  141  160
    ## [1] "Na_max EDA:"
    ## [1] "Number of non-missing values: 2061"
    ## [1] "Number of missing values: 0"
    ##   0%  25%  50%  75% 100% 
    ##  112  137  140  142  177
    ## [1] "NISysABP_min EDA:"
    ## [1] "Number of non-missing values: 1608"
    ## [1] "Number of missing values: 453"
    ##   0%  25%  50%  75% 100% 
    ##    4   83   95  108  234
    ## [1] "NISysABP_max EDA:"
    ## [1] "Number of non-missing values: 1608"
    ## [1] "Number of missing values: 453"
    ##   0%  25%  50%  75% 100% 
    ##   78  121  138  156  274
    ## [1] "Platelets_min EDA:"
    ## [1] "Number of non-missing values: 2061"
    ## [1] "Number of missing values: 0"
    ##   0%  25%  50%  75% 100% 
    ##    9  126  184  246  891
    ## [1] "PFratio EDA:"
    ## [1] "Number of non-missing values: 2061"
    ## [1] "Number of missing values: 0"
    ##   0%  25%  50%  75% 100% 
    ##   24   85  122  188 1150
    ## [1] "pH_min EDA:"
    ## [1] "Number of non-missing values: 2061"
    ## [1] "Number of missing values: 0"
    ##   0%  25%  50%  75% 100% 
    ## 3.00 7.28 7.34 7.39 7.63
    ## [1] "pH_max EDA:"
    ## [1] "Number of non-missing values: 2061"
    ## [1] "Number of missing values: 0"
    ##   0%  25%  50%  75% 100% 
    ## 7.15 7.38 7.42 7.46 7.69
    ## [1] "RespRate_min EDA:"
    ## [1] "Number of non-missing values: 2061"
    ## [1] "Number of missing values: 0"
    ##   0%  25%  50%  75% 100% 
    ##    4   12   14   17   24
    ## [1] "RespRate_max EDA:"
    ## [1] "Number of non-missing values: 2061"
    ## [1] "Number of missing values: 0"
    ##   0%  25%  50%  75% 100% 
    ##   13   24   27   33   98
    ## [1] "Temp_min EDA:"
    ## [1] "Number of non-missing values: 2061"
    ## [1] "Number of missing values: 0"
    ##   0%  25%  50%  75% 100% 
    ## 24.2 35.6 36.1 36.6 38.3
    ## [1] "Temp_max EDA:"
    ## [1] "Number of non-missing values: 2061"
    ## [1] "Number of missing values: 0"
    ##   0%  25%  50%  75% 100% 
    ## 35.4 37.1 37.6 38.2 42.1
    ## [1] "TroponinI_max EDA:"
    ## [1] "Number of non-missing values: 2061"
    ## [1] "Number of missing values: 0"
    ##   0%  25%  50%  75% 100% 
    ##  0.3  2.6  7.8 17.6 43.4
    ## [1] "TroponinT_max EDA:"
    ## [1] "Number of non-missing values: 2061"
    ## [1] "Number of missing values: 0"
    ##    0%   25%   50%   75%  100% 
    ##  0.01  0.06  0.17  0.80 24.46
    ## [1] "Urine_min EDA:"
    ## [1] "Number of non-missing values: 2061"
    ## [1] "Number of missing values: 0"
    ##   0%  25%  50%  75% 100% 
    ##    0    0   20   36  600
    ## [1] "WBC_min EDA:"
    ## [1] "Number of non-missing values: 2061"
    ## [1] "Number of missing values: 0"
    ##    0%   25%   50%   75%  100% 
    ##   0.1   7.6  10.4  14.1 128.3
    ## [1] "WBC_max EDA:"
    ## [1] "Number of non-missing values: 2061"
    ## [1] "Number of missing values: 0"
    ##    0%   25%   50%   75%  100% 
    ##   0.1   9.3  12.3  16.9 155.6

    *** needs to be updated: ***

    ** EDA Findings

    • There are 2061 unique individuals in the dataset. Of these, 913 are female (44%) and 1148 are male (56%).
    • Medical ICU accounted for 38% of individuals, 26% in Surgical ICU, 24% in Cardiac Surgery recovery Unit and 14% in the Coronary Care unit.
    • The median length of stay in hospital is 10 days with an IQ range of 11 days. There are 25 missing values.
    • The median age is 67 with an IQ range of 26.
    • The median height is 170.2 cm with IQ range of 15.2cm. There are 1069 (52%) with a valid measurements.
    • The median minimum weight is 77.7 kg with a IQ range of 26.95. The median maximum weight is 80kg (slightly higher) with an IQ range of 28.55. The median difference in weight (max to mean over 24 hrs) is 14.7 kg with an IQ range of 17.2 kg. Some outliers or measurement error looks present with a max difference on 149kg.

    • The median minimum Bilirubin is 0.6 with an IQ range of 0.7. The median maximum Bilirubin is 0.7 with an IQ range of 0.9. The median difference in Bilirubin is 1.36 with an IQ range of 0.4.
    • The median minimum Creatinine is 0.9 with an IQ range of 0.6. The median maximum Creatinine is 1.0 with an IQ range of 0.7. The median difference in Creatinine is 0.53 with an IQ range of 0.4.

    … fill out the rest….

    #Plot the Kaplan-Meier survival curves by all categorical variables in the data
    
    #Gender
    ICU.gender.fit <- survfit( Surv(Days, Status) ~ as.factor(Gender), data = icu_patients_df1) 
    print(ICU.gender.fit, print.rmean = TRUE)
    ## Call: survfit(formula = Surv(Days, Status) ~ as.factor(Gender), data = icu_patients_df1)
    ## 
    ##                             n events *rmean *se(rmean) median 0.95LCL 0.95UCL
    ## as.factor(Gender)=Female  913    364   1588       35.2     NA      NA      NA
    ## as.factor(Gender)=Male   1148    409   1670       30.6     NA      NA      NA
    ##     * restricted mean with upper limit =  2408
    plot(ICU.gender.fit, col=c("blue", "red"), main = 'Kaplan-Meier estimate of survival function', xlab = 'Length of survival (in days)')
    legend("bottomleft", legend=c("Female", "Male"),col=c("blue","red"), lty=1:1,cex=1)

    #ICUType
    ICU.type.fit <- survfit( Surv(Days, Status) ~ as.factor(ICUType), data = icu_patients_df1) 
    print(ICU.type.fit, print.rmean = TRUE)
    ## Call: survfit(formula = Surv(Days, Status) ~ as.factor(ICUType), data = icu_patients_df1)
    ## 
    ##                                                    n events *rmean *se(rmean)
    ## as.factor(ICUType)=Coronary Care Unit            297    132   1486       63.1
    ## as.factor(ICUType)=Cardiac Surgery Recovery Unit 448     99   2002       38.9
    ## as.factor(ICUType)=Medical ICU                   788    372   1414       39.3
    ## as.factor(ICUType)=Surgical ICU                  528    170   1731       44.3
    ##                                                  median 0.95LCL 0.95UCL
    ## as.factor(ICUType)=Coronary Care Unit                NA      NA      NA
    ## as.factor(ICUType)=Cardiac Surgery Recovery Unit     NA      NA      NA
    ## as.factor(ICUType)=Medical ICU                       NA    2051      NA
    ## as.factor(ICUType)=Surgical ICU                      NA      NA      NA
    ##     * restricted mean with upper limit =  2408
    plot(ICU.type.fit, col=c("blue", "red","purple","green"), main = 'Kaplan-Meier estimate of survival function', xlab = 'Length of survival (in days)')
    legend("bottomleft", legend=c("Coronary Care Unit", "Cardiac Surgery Recovery Unit", "Medical ICU", "Surgical ICU"),col=c("blue","red","purple","green"), lty=1:1,cex=1)

    Risk of mortality is different by both Gender and ICU Type - the hazard rates also look proportional.

    1. Fit appropriate univariate Cox proportional hazards models.
    # Cox proportional models and Log Rank tests for the chosen variables
    # Survival object = Surv(Days, Status)
    
    # Gender
    ICU.fitbyGender <- coxph( Surv(Days, Status) ~ as.factor(Gender), data = icu_patients_df1) 
    summary(ICU.fitbyGender)
    ## Call:
    ## coxph(formula = Surv(Days, Status) ~ as.factor(Gender), data = icu_patients_df1)
    ## 
    ##   n= 2061, number of events= 773 
    ## 
    ##                           coef exp(coef) se(coef)      z Pr(>|z|)  
    ## as.factor(Gender)Male -0.13708   0.87190  0.07206 -1.902   0.0571 .
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ## 
    ##                       exp(coef) exp(-coef) lower .95 upper .95
    ## as.factor(Gender)Male    0.8719      1.147    0.7571     1.004
    ## 
    ## Concordance= 0.516  (se = 0.009 )
    ## Likelihood ratio test= 3.61  on 1 df,   p=0.06
    ## Wald test            = 3.62  on 1 df,   p=0.06
    ## Score (logrank) test = 3.62  on 1 df,   p=0.06
    # ICU Type
    ICU.fitbytype <- coxph( Surv(Days, Status) ~ as.factor(ICUType), data = icu_patients_df1) 
    summary(ICU.fitbytype)
    ## Call:
    ## coxph(formula = Surv(Days, Status) ~ as.factor(ICUType), data = icu_patients_df1)
    ## 
    ##   n= 2061, number of events= 773 
    ## 
    ##                                                     coef exp(coef) se(coef)
    ## as.factor(ICUType)Cardiac Surgery Recovery Unit -0.87895   0.41522  0.13301
    ## as.factor(ICUType)Medical ICU                    0.09362   1.09815  0.10131
    ## as.factor(ICUType)Surgical ICU                  -0.39843   0.67137  0.11603
    ##                                                      z        Pr(>|z|)    
    ## as.factor(ICUType)Cardiac Surgery Recovery Unit -6.608 0.0000000000389 ***
    ## as.factor(ICUType)Medical ICU                    0.924        0.355437    
    ## as.factor(ICUType)Surgical ICU                  -3.434        0.000595 ***
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ## 
    ##                                                 exp(coef) exp(-coef) lower .95
    ## as.factor(ICUType)Cardiac Surgery Recovery Unit    0.4152     2.4084    0.3199
    ## as.factor(ICUType)Medical ICU                      1.0981     0.9106    0.9004
    ## as.factor(ICUType)Surgical ICU                     0.6714     1.4895    0.5348
    ##                                                 upper .95
    ## as.factor(ICUType)Cardiac Surgery Recovery Unit    0.5389
    ## as.factor(ICUType)Medical ICU                      1.3394
    ## as.factor(ICUType)Surgical ICU                     0.8428
    ## 
    ## Concordance= 0.597  (se = 0.009 )
    ## Likelihood ratio test= 98.74  on 3 df,   p=<0.0000000000000002
    ## Wald test            = 87.96  on 3 df,   p=<0.0000000000000002
    ## Score (logrank) test = 93.02  on 3 df,   p=<0.0000000000000002
    # Age
    ICU.fitbyage <- coxph( Surv(Days, Status) ~ Age, data = icu_patients_df1) 
    summary(ICU.fitbyage)
    ## Call:
    ## coxph(formula = Surv(Days, Status) ~ Age, data = icu_patients_df1)
    ## 
    ##   n= 2061, number of events= 773 
    ## 
    ##        coef exp(coef) se(coef)     z            Pr(>|z|)    
    ## Age 0.03355   1.03412  0.00250 13.42 <0.0000000000000002 ***
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ## 
    ##     exp(coef) exp(-coef) lower .95 upper .95
    ## Age     1.034      0.967     1.029     1.039
    ## 
    ## Concordance= 0.646  (se = 0.01 )
    ## Likelihood ratio test= 209.4  on 1 df,   p=<0.0000000000000002
    ## Wald test            = 180.1  on 1 df,   p=<0.0000000000000002
    ## Score (logrank) test = 187  on 1 df,   p=<0.0000000000000002
    # Height
    ICU.fitbyheight <- coxph( Surv(Days, Status) ~ Height, data = icu_patients_df1) 
    summary(ICU.fitbyheight)
    ## Call:
    ## coxph(formula = Surv(Days, Status) ~ Height, data = icu_patients_df1)
    ## 
    ##   n= 1069, number of events= 385 
    ##    (992 observations deleted due to missingness)
    ## 
    ##             coef exp(coef)  se(coef)      z Pr(>|z|)
    ## Height -0.003851  0.996156  0.002346 -1.642    0.101
    ## 
    ##        exp(coef) exp(-coef) lower .95 upper .95
    ## Height    0.9962      1.004    0.9916     1.001
    ## 
    ## Concordance= 0.541  (se = 0.015 )
    ## Likelihood ratio test= 2.7  on 1 df,   p=0.1
    ## Wald test            = 2.69  on 1 df,   p=0.1
    ## Score (logrank) test = 2.52  on 1 df,   p=0.1
    # Weight_max
    ICU.fitbyweightmax <- coxph( Surv(Days, Status) ~ Weight_max, data = icu_patients_df1) 
    summary(ICU.fitbyweightmax)
    ## Call:
    ## coxph(formula = Surv(Days, Status) ~ Weight_max, data = icu_patients_df1)
    ## 
    ##   n= 1915, number of events= 721 
    ##    (146 observations deleted due to missingness)
    ## 
    ##                 coef exp(coef)  se(coef)      z  Pr(>|z|)    
    ## Weight_max -0.007213  0.992813  0.001759 -4.101 0.0000411 ***
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ## 
    ##            exp(coef) exp(-coef) lower .95 upper .95
    ## Weight_max    0.9928      1.007    0.9894    0.9962
    ## 
    ## Concordance= 0.56  (se = 0.011 )
    ## Likelihood ratio test= 17.9  on 1 df,   p=0.00002
    ## Wald test            = 16.82  on 1 df,   p=0.00004
    ## Score (logrank) test = 16.71  on 1 df,   p=0.00004
    # Albumin_min
    ICU.fitbyAlbuminmin <- coxph( Surv(Days, Status) ~ Albumin_min, data = icu_patients_df1) 
    summary(ICU.fitbyAlbuminmin)
    ## Call:
    ## coxph(formula = Surv(Days, Status) ~ Albumin_min, data = icu_patients_df1)
    ## 
    ##   n= 2061, number of events= 773 
    ## 
    ##                 coef exp(coef) se(coef)     z Pr(>|z|)    
    ## Albumin_min -0.22075   0.80192  0.05704 -3.87 0.000109 ***
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ## 
    ##             exp(coef) exp(-coef) lower .95 upper .95
    ## Albumin_min    0.8019      1.247    0.7171    0.8968
    ## 
    ## Concordance= 0.54  (se = 0.011 )
    ## Likelihood ratio test= 15.02  on 1 df,   p=0.0001
    ## Wald test            = 14.98  on 1 df,   p=0.0001
    ## Score (logrank) test = 14.99  on 1 df,   p=0.0001
    # Bilirubin_max
    ICU.fitbyBilirubinmax <- coxph( Surv(Days, Status) ~ Bilirubin_max, data = icu_patients_df1) 
    summary(ICU.fitbyBilirubinmax)
    ## Call:
    ## coxph(formula = Surv(Days, Status) ~ Bilirubin_max, data = icu_patients_df1)
    ## 
    ##   n= 2061, number of events= 773 
    ## 
    ##                   coef exp(coef) se(coef)     z Pr(>|z|)    
    ## Bilirubin_max 0.025159  1.025478 0.007431 3.386  0.00071 ***
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ## 
    ##               exp(coef) exp(-coef) lower .95 upper .95
    ## Bilirubin_max     1.025     0.9752     1.011     1.041
    ## 
    ## Concordance= 0.515  (se = 0.011 )
    ## Likelihood ratio test= 9.48  on 1 df,   p=0.002
    ## Wald test            = 11.46  on 1 df,   p=0.0007
    ## Score (logrank) test = 11.7  on 1 df,   p=0.0006
    # BUN_max
    ICU.fitbyBUNmax <- coxph( Surv(Days, Status) ~ BUN_max, data = icu_patients_df1) 
    summary(ICU.fitbyBUNmax)
    ## Call:
    ## coxph(formula = Surv(Days, Status) ~ BUN_max, data = icu_patients_df1)
    ## 
    ##   n= 2061, number of events= 773 
    ## 
    ##             coef exp(coef) se(coef)     z            Pr(>|z|)    
    ## BUN_max 0.015002  1.015115 0.001064 14.09 <0.0000000000000002 ***
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ## 
    ##         exp(coef) exp(-coef) lower .95 upper .95
    ## BUN_max     1.015     0.9851     1.013     1.017
    ## 
    ## Concordance= 0.647  (se = 0.01 )
    ## Likelihood ratio test= 142.5  on 1 df,   p=<0.0000000000000002
    ## Wald test            = 198.6  on 1 df,   p=<0.0000000000000002
    ## Score (logrank) test = 207  on 1 df,   p=<0.0000000000000002
    # Creatinine_max
    ICU.fitbyCreatininemax <- coxph( Surv(Days, Status) ~ Creatinine_max, data = icu_patients_df1) 
    summary(ICU.fitbyCreatininemax)
    ## Call:
    ## coxph(formula = Surv(Days, Status) ~ Creatinine_max, data = icu_patients_df1)
    ## 
    ##   n= 2061, number of events= 773 
    ## 
    ##                   coef exp(coef) se(coef)    z        Pr(>|z|)    
    ## Creatinine_max 0.10152   1.10685  0.01467 6.92 0.0000000000045 ***
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ## 
    ##                exp(coef) exp(-coef) lower .95 upper .95
    ## Creatinine_max     1.107     0.9035     1.075     1.139
    ## 
    ## Concordance= 0.594  (se = 0.011 )
    ## Likelihood ratio test= 35.11  on 1 df,   p=0.000000003
    ## Wald test            = 47.89  on 1 df,   p=0.000000000005
    ## Score (logrank) test = 48.54  on 1 df,   p=0.000000000003
    # GCS_min
    ICU.fitbyGCSmin <- coxph( Surv(Days, Status) ~ GCS_min, data = icu_patients_df1) 
    summary(ICU.fitbyGCSmin)
    ## Call:
    ## coxph(formula = Surv(Days, Status) ~ GCS_min, data = icu_patients_df1)
    ## 
    ##   n= 2061, number of events= 773 
    ## 
    ##             coef exp(coef) se(coef)     z Pr(>|z|)
    ## GCS_min 0.006052  1.006070 0.007324 0.826    0.409
    ## 
    ##         exp(coef) exp(-coef) lower .95 upper .95
    ## GCS_min     1.006      0.994    0.9917     1.021
    ## 
    ## Concordance= 0.501  (se = 0.01 )
    ## Likelihood ratio test= 0.68  on 1 df,   p=0.4
    ## Wald test            = 0.68  on 1 df,   p=0.4
    ## Score (logrank) test = 0.68  on 1 df,   p=0.4
    # Glucose - min & max
    ICU.fitbyGlucosemin <- coxph( Surv(Days, Status) ~ Glucose_min, data = icu_patients_df1) 
    summary(ICU.fitbyGlucosemin)
    ## Call:
    ## coxph(formula = Surv(Days, Status) ~ Glucose_min, data = icu_patients_df1)
    ## 
    ##   n= 2061, number of events= 773 
    ## 
    ##                  coef exp(coef)  se(coef)     z Pr(>|z|)  
    ## Glucose_min 0.0014076 1.0014086 0.0007477 1.883   0.0597 .
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ## 
    ##             exp(coef) exp(-coef) lower .95 upper .95
    ## Glucose_min     1.001     0.9986    0.9999     1.003
    ## 
    ## Concordance= 0.508  (se = 0.011 )
    ## Likelihood ratio test= 3.31  on 1 df,   p=0.07
    ## Wald test            = 3.54  on 1 df,   p=0.06
    ## Score (logrank) test = 3.53  on 1 df,   p=0.06
    ICU.fitbyGlucosemax <- coxph( Surv(Days, Status) ~ Glucose_max, data = icu_patients_df1) 
    summary(ICU.fitbyGlucosemax)
    ## Call:
    ## coxph(formula = Surv(Days, Status) ~ Glucose_max, data = icu_patients_df1)
    ## 
    ##   n= 2061, number of events= 773 
    ## 
    ##                  coef exp(coef)  se(coef) z  Pr(>|z|)    
    ## Glucose_max 0.0012981 1.0012989 0.0003245 4 0.0000634 ***
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ## 
    ##             exp(coef) exp(-coef) lower .95 upper .95
    ## Glucose_max     1.001     0.9987     1.001     1.002
    ## 
    ## Concordance= 0.547  (se = 0.011 )
    ## Likelihood ratio test= 13.2  on 1 df,   p=0.0003
    ## Wald test            = 16  on 1 df,   p=0.00006
    ## Score (logrank) test = 15.96  on 1 df,   p=0.00006
    # HCO3_min
    ICU.fitbyHCO3min <- coxph( Surv(Days, Status) ~ HCO3_min, data = icu_patients_df1) 
    summary(ICU.fitbyHCO3min)
    ## Call:
    ## coxph(formula = Surv(Days, Status) ~ HCO3_min, data = icu_patients_df1)
    ## 
    ##   n= 2061, number of events= 773 
    ## 
    ##               coef exp(coef)  se(coef)      z Pr(>|z|)  
    ## HCO3_min -0.017036  0.983108  0.008023 -2.123   0.0337 *
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ## 
    ##          exp(coef) exp(-coef) lower .95 upper .95
    ## HCO3_min    0.9831      1.017    0.9678    0.9987
    ## 
    ## Concordance= 0.535  (se = 0.011 )
    ## Likelihood ratio test= 4.49  on 1 df,   p=0.03
    ## Wald test            = 4.51  on 1 df,   p=0.03
    ## Score (logrank) test = 4.5  on 1 df,   p=0.03
    # HR - min & max
    ICU.fitbyHRmin <- coxph( Surv(Days, Status) ~ HR_min, data = icu_patients_df1) 
    summary(ICU.fitbyHRmin)
    ## Call:
    ## coxph(formula = Surv(Days, Status) ~ HR_min, data = icu_patients_df1)
    ## 
    ##   n= 2061, number of events= 773 
    ## 
    ##              coef  exp(coef)   se(coef)      z Pr(>|z|)
    ## HR_min -0.0009841  0.9990164  0.0024165 -0.407    0.684
    ## 
    ##        exp(coef) exp(-coef) lower .95 upper .95
    ## HR_min     0.999      1.001    0.9943     1.004
    ## 
    ## Concordance= 0.498  (se = 0.011 )
    ## Likelihood ratio test= 0.17  on 1 df,   p=0.7
    ## Wald test            = 0.17  on 1 df,   p=0.7
    ## Score (logrank) test = 0.17  on 1 df,   p=0.7
    ICU.fitbyHRmax <- coxph( Surv(Days, Status) ~ HR_max, data = icu_patients_df1) 
    summary(ICU.fitbyHRmax)
    ## Call:
    ## coxph(formula = Surv(Days, Status) ~ HR_max, data = icu_patients_df1)
    ## 
    ##   n= 2061, number of events= 773 
    ## 
    ##            coef exp(coef) se(coef)     z Pr(>|z|)  
    ## HR_max 0.002779  1.002783 0.001648 1.687   0.0916 .
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ## 
    ##        exp(coef) exp(-coef) lower .95 upper .95
    ## HR_max     1.003     0.9972    0.9996     1.006
    ## 
    ## Concordance= 0.515  (se = 0.011 )
    ## Likelihood ratio test= 2.79  on 1 df,   p=0.09
    ## Wald test            = 2.85  on 1 df,   p=0.09
    ## Score (logrank) test = 2.84  on 1 df,   p=0.09
    # K - min & max
    ICU.fitbyKmin <- coxph( Surv(Days, Status) ~ K_min, data = icu_patients_df1) 
    summary(ICU.fitbyKmin)
    ## Call:
    ## coxph(formula = Surv(Days, Status) ~ K_min, data = icu_patients_df1)
    ## 
    ##   n= 2061, number of events= 773 
    ## 
    ##          coef exp(coef) se(coef)     z Pr(>|z|)
    ## K_min 0.03906   1.03983  0.06125 0.638    0.524
    ## 
    ##       exp(coef) exp(-coef) lower .95 upper .95
    ## K_min      1.04     0.9617    0.9222     1.172
    ## 
    ## Concordance= 0.502  (se = 0.011 )
    ## Likelihood ratio test= 0.41  on 1 df,   p=0.5
    ## Wald test            = 0.41  on 1 df,   p=0.5
    ## Score (logrank) test = 0.41  on 1 df,   p=0.5
    ICU.fitbyKmax <- coxph( Surv(Days, Status) ~ K_max, data = icu_patients_df1) 
    summary(ICU.fitbyKmax)
    ## Call:
    ## coxph(formula = Surv(Days, Status) ~ K_max, data = icu_patients_df1)
    ## 
    ##   n= 2061, number of events= 773 
    ## 
    ##          coef exp(coef) se(coef)     z Pr(>|z|)  
    ## K_max 0.07306   1.07579  0.02958 2.469   0.0135 *
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ## 
    ##       exp(coef) exp(-coef) lower .95 upper .95
    ## K_max     1.076     0.9295     1.015      1.14
    ## 
    ## Concordance= 0.527  (se = 0.011 )
    ## Likelihood ratio test= 4.81  on 1 df,   p=0.03
    ## Wald test            = 6.1  on 1 df,   p=0.01
    ## Score (logrank) test = 5.98  on 1 df,   p=0.01
    # Lactate_max
    ICU.fitbyLactatemax <- coxph( Surv(Days, Status) ~ Lactate_max, data = icu_patients_df1) 
    summary(ICU.fitbyLactatemax)
    ## Call:
    ## coxph(formula = Surv(Days, Status) ~ Lactate_max, data = icu_patients_df1)
    ## 
    ##   n= 2061, number of events= 773 
    ## 
    ##                coef exp(coef) se(coef)     z Pr(>|z|)    
    ## Lactate_max 0.05778   1.05948  0.01666 3.467 0.000526 ***
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ## 
    ##             exp(coef) exp(-coef) lower .95 upper .95
    ## Lactate_max     1.059     0.9439     1.025     1.095
    ## 
    ## Concordance= 0.508  (se = 0.011 )
    ## Likelihood ratio test= 10.95  on 1 df,   p=0.0009
    ## Wald test            = 12.02  on 1 df,   p=0.0005
    ## Score (logrank) test = 12.03  on 1 df,   p=0.0005
    # MAP_min
    ICU.fitbyMAPmin <- coxph( Surv(Days, Status) ~ MAP_min, data = icu_patients_df1) 
    summary(ICU.fitbyMAPmin)
    ## Call:
    ## coxph(formula = Surv(Days, Status) ~ MAP_min, data = icu_patients_df1)
    ## 
    ##   n= 2061, number of events= 773 
    ## 
    ##              coef exp(coef)  se(coef)     z Pr(>|z|)  
    ## MAP_min -0.004744  0.995267  0.002326 -2.04   0.0414 *
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ## 
    ##         exp(coef) exp(-coef) lower .95 upper .95
    ## MAP_min    0.9953      1.005    0.9907    0.9998
    ## 
    ## Concordance= 0.52  (se = 0.01 )
    ## Likelihood ratio test= 4.37  on 1 df,   p=0.04
    ## Wald test            = 4.16  on 1 df,   p=0.04
    ## Score (logrank) test = 4.07  on 1 df,   p=0.04
    # Na - min & max
    ICU.fitbyNamin <- coxph( Surv(Days, Status) ~ Na_min, data = icu_patients_df1) 
    summary(ICU.fitbyNamin)
    ## Call:
    ## coxph(formula = Surv(Days, Status) ~ Na_min, data = icu_patients_df1)
    ## 
    ##   n= 2061, number of events= 773 
    ## 
    ##             coef exp(coef)  se(coef)      z Pr(>|z|)   
    ## Na_min -0.021187  0.979036  0.007371 -2.875  0.00405 **
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ## 
    ##        exp(coef) exp(-coef) lower .95 upper .95
    ## Na_min     0.979      1.021     0.965    0.9933
    ## 
    ## Concordance= 0.536  (se = 0.011 )
    ## Likelihood ratio test= 7.74  on 1 df,   p=0.005
    ## Wald test            = 8.26  on 1 df,   p=0.004
    ## Score (logrank) test = 8.16  on 1 df,   p=0.004
    ICU.fitbyNamax <- coxph( Surv(Days, Status) ~ Na_max, data = icu_patients_df1) 
    summary(ICU.fitbyNamax)
    ## Call:
    ## coxph(formula = Surv(Days, Status) ~ Na_max, data = icu_patients_df1)
    ## 
    ##   n= 2061, number of events= 773 
    ## 
    ##             coef exp(coef)  se(coef)      z Pr(>|z|)  
    ## Na_max -0.015698  0.984424  0.008287 -1.894   0.0582 .
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ## 
    ##        exp(coef) exp(-coef) lower .95 upper .95
    ## Na_max    0.9844      1.016    0.9686     1.001
    ## 
    ## Concordance= 0.521  (se = 0.011 )
    ## Likelihood ratio test= 3.61  on 1 df,   p=0.06
    ## Wald test            = 3.59  on 1 df,   p=0.06
    ## Score (logrank) test = 3.57  on 1 df,   p=0.06
    # NISysABP - min & max
    ICU.fitbyNISysABPmin <- coxph( Surv(Days, Status) ~ NISysABP_min, data = icu_patients_df1) 
    summary(ICU.fitbyNISysABPmin)
    ## Call:
    ## coxph(formula = Surv(Days, Status) ~ NISysABP_min, data = icu_patients_df1)
    ## 
    ##   n= 1608, number of events= 651 
    ##    (453 observations deleted due to missingness)
    ## 
    ##                   coef exp(coef)  se(coef)      z Pr(>|z|)    
    ## NISysABP_min -0.007374  0.992653  0.001994 -3.699 0.000216 ***
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ## 
    ##              exp(coef) exp(-coef) lower .95 upper .95
    ## NISysABP_min    0.9927      1.007    0.9888    0.9965
    ## 
    ## Concordance= 0.555  (se = 0.012 )
    ## Likelihood ratio test= 14  on 1 df,   p=0.0002
    ## Wald test            = 13.68  on 1 df,   p=0.0002
    ## Score (logrank) test = 13.54  on 1 df,   p=0.0002
    ICU.fitbyNISysABPmax <- coxph( Surv(Days, Status) ~ NISysABP_max, data = icu_patients_df1) 
    summary(ICU.fitbyNISysABPmax)
    ## Call:
    ## coxph(formula = Surv(Days, Status) ~ NISysABP_max, data = icu_patients_df1)
    ## 
    ##   n= 1608, number of events= 651 
    ##    (453 observations deleted due to missingness)
    ## 
    ##                  coef exp(coef) se(coef)     z Pr(>|z|)  
    ## NISysABP_max 0.003503  1.003509 0.001402 2.498   0.0125 *
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ## 
    ##              exp(coef) exp(-coef) lower .95 upper .95
    ## NISysABP_max     1.004     0.9965     1.001     1.006
    ## 
    ## Concordance= 0.523  (se = 0.012 )
    ## Likelihood ratio test= 6.12  on 1 df,   p=0.01
    ## Wald test            = 6.24  on 1 df,   p=0.01
    ## Score (logrank) test = 6.24  on 1 df,   p=0.01
    # Platelets_min
    ICU.fitbyPlateletsmin <- coxph( Surv(Days, Status) ~ Platelets_min, data = icu_patients_df1) 
    summary(ICU.fitbyPlateletsmin)
    ## Call:
    ## coxph(formula = Surv(Days, Status) ~ Platelets_min, data = icu_patients_df1)
    ## 
    ##   n= 2061, number of events= 773 
    ## 
    ##                    coef exp(coef)  se(coef)     z Pr(>|z|)
    ## Platelets_min 0.0001735 1.0001735 0.0003440 0.504    0.614
    ## 
    ##               exp(coef) exp(-coef) lower .95 upper .95
    ## Platelets_min         1     0.9998    0.9995     1.001
    ## 
    ## Concordance= 0.499  (se = 0.011 )
    ## Likelihood ratio test= 0.25  on 1 df,   p=0.6
    ## Wald test            = 0.25  on 1 df,   p=0.6
    ## Score (logrank) test = 0.25  on 1 df,   p=0.6
    # PFratio (PaO2_min/FiO2_max)
    ICU.fitbyPFratio <- coxph( Surv(Days, Status) ~ PFratio, data = icu_patients_df1) 
    summary(ICU.fitbyPFratio)
    ## Call:
    ## coxph(formula = Surv(Days, Status) ~ PFratio, data = icu_patients_df1)
    ## 
    ##   n= 2061, number of events= 773 
    ## 
    ##               coef  exp(coef)   se(coef)     z Pr(>|z|)
    ## PFratio -0.0002469  0.9997531  0.0003579 -0.69     0.49
    ## 
    ##         exp(coef) exp(-coef) lower .95 upper .95
    ## PFratio    0.9998          1    0.9991         1
    ## 
    ## Concordance= 0.513  (se = 0.011 )
    ## Likelihood ratio test= 0.49  on 1 df,   p=0.5
    ## Wald test            = 0.48  on 1 df,   p=0.5
    ## Score (logrank) test = 0.48  on 1 df,   p=0.5
    # pH - min & max
    ICU.fitbypHmin <- coxph( Surv(Days, Status) ~ pH_min, data = icu_patients_df1) 
    summary(ICU.fitbypHmin)
    ## Call:
    ## coxph(formula = Surv(Days, Status) ~ pH_min, data = icu_patients_df1)
    ## 
    ##   n= 2061, number of events= 773 
    ## 
    ##           coef exp(coef) se(coef)      z Pr(>|z|)    
    ## pH_min -0.6668    0.5133   0.1717 -3.884 0.000103 ***
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ## 
    ##        exp(coef) exp(-coef) lower .95 upper .95
    ## pH_min    0.5133      1.948    0.3667    0.7187
    ## 
    ## Concordance= 0.51  (se = 0.011 )
    ## Likelihood ratio test= 8.34  on 1 df,   p=0.004
    ## Wald test            = 15.09  on 1 df,   p=0.0001
    ## Score (logrank) test = 14.09  on 1 df,   p=0.0002
    ICU.fitbypHmax <- coxph( Surv(Days, Status) ~ pH_max, data = icu_patients_df1) 
    summary(ICU.fitbypHmax)
    ## Call:
    ## coxph(formula = Surv(Days, Status) ~ pH_max, data = icu_patients_df1)
    ## 
    ##   n= 2061, number of events= 773 
    ## 
    ##           coef exp(coef) se(coef)      z Pr(>|z|)  
    ## pH_max -1.3288    0.2648   0.5512 -2.411   0.0159 *
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ## 
    ##        exp(coef) exp(-coef) lower .95 upper .95
    ## pH_max    0.2648      3.776    0.0899      0.78
    ## 
    ## Concordance= 0.524  (se = 0.011 )
    ## Likelihood ratio test= 5.78  on 1 df,   p=0.02
    ## Wald test            = 5.81  on 1 df,   p=0.02
    ## Score (logrank) test = 5.81  on 1 df,   p=0.02
    # RespRate - min & max
    ICU.fitbyRespRatemin <- coxph( Surv(Days, Status) ~ RespRate_min, data = icu_patients_df1) 
    summary(ICU.fitbyRespRatemin)
    ## Call:
    ## coxph(formula = Surv(Days, Status) ~ RespRate_min, data = icu_patients_df1)
    ## 
    ##   n= 2061, number of events= 773 
    ## 
    ##                  coef exp(coef) se(coef)     z   Pr(>|z|)    
    ## RespRate_min 0.042945  1.043880 0.009451 4.544 0.00000552 ***
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ## 
    ##              exp(coef) exp(-coef) lower .95 upper .95
    ## RespRate_min     1.044      0.958     1.025     1.063
    ## 
    ## Concordance= 0.555  (se = 0.01 )
    ## Likelihood ratio test= 20.44  on 1 df,   p=0.000006
    ## Wald test            = 20.65  on 1 df,   p=0.000006
    ## Score (logrank) test = 20.67  on 1 df,   p=0.000005
    ICU.fitbyRespRatemax <- coxph( Surv(Days, Status) ~ RespRate_max, data = icu_patients_df1) 
    summary(ICU.fitbyRespRatemax)
    ## Call:
    ## coxph(formula = Surv(Days, Status) ~ RespRate_max, data = icu_patients_df1)
    ## 
    ##   n= 2061, number of events= 773 
    ## 
    ##                 coef exp(coef) se(coef)     z Pr(>|z|)    
    ## RespRate_max 0.01472   1.01483  0.00432 3.407 0.000657 ***
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ## 
    ##              exp(coef) exp(-coef) lower .95 upper .95
    ## RespRate_max     1.015     0.9854     1.006     1.023
    ## 
    ## Concordance= 0.535  (se = 0.011 )
    ## Likelihood ratio test= 10.93  on 1 df,   p=0.0009
    ## Wald test            = 11.61  on 1 df,   p=0.0007
    ## Score (logrank) test = 11.54  on 1 df,   p=0.0007
    # Temp - min & max
    ICU.fitbyTempmin <- coxph( Surv(Days, Status) ~ Temp_min, data = icu_patients_df1) 
    summary(ICU.fitbyTempmin)
    ## Call:
    ## coxph(formula = Surv(Days, Status) ~ Temp_min, data = icu_patients_df1)
    ## 
    ##   n= 2061, number of events= 773 
    ## 
    ##              coef exp(coef) se(coef)      z Pr(>|z|)   
    ## Temp_min -0.10541   0.89996  0.03894 -2.707  0.00679 **
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ## 
    ##          exp(coef) exp(-coef) lower .95 upper .95
    ## Temp_min       0.9      1.111    0.8338    0.9713
    ## 
    ## Concordance= 0.528  (se = 0.011 )
    ## Likelihood ratio test= 6.85  on 1 df,   p=0.009
    ## Wald test            = 7.33  on 1 df,   p=0.007
    ## Score (logrank) test = 7.21  on 1 df,   p=0.007
    ICU.fitbyTempmax <- coxph( Surv(Days, Status) ~ Temp_max, data = icu_patients_df1) 
    summary(ICU.fitbyTempmax)
    ## Call:
    ## coxph(formula = Surv(Days, Status) ~ Temp_max, data = icu_patients_df1)
    ## 
    ##   n= 2061, number of events= 773 
    ## 
    ##             coef exp(coef) se(coef)      z  Pr(>|z|)    
    ## Temp_max -0.1966    0.8215   0.0493 -3.988 0.0000668 ***
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ## 
    ##          exp(coef) exp(-coef) lower .95 upper .95
    ## Temp_max    0.8215      1.217    0.7459    0.9049
    ## 
    ## Concordance= 0.55  (se = 0.011 )
    ## Likelihood ratio test= 16.34  on 1 df,   p=0.00005
    ## Wald test            = 15.9  on 1 df,   p=0.00007
    ## Score (logrank) test = 15.89  on 1 df,   p=0.00007
    # Troponin_max (I and T assays)
    ICU.fitbyTroponinImax <- coxph( Surv(Days, Status) ~ TroponinI_max, data = icu_patients_df1) 
    summary(ICU.fitbyTroponinImax)
    ## Call:
    ## coxph(formula = Surv(Days, Status) ~ TroponinI_max, data = icu_patients_df1)
    ## 
    ##   n= 2061, number of events= 773 
    ## 
    ##                      coef   exp(coef)    se(coef)      z Pr(>|z|)
    ## TroponinI_max -0.00000905  0.99999095  0.00324098 -0.003    0.998
    ## 
    ##               exp(coef) exp(-coef) lower .95 upper .95
    ## TroponinI_max         1          1    0.9937     1.006
    ## 
    ## Concordance= 0.508  (se = 0.011 )
    ## Likelihood ratio test= 0  on 1 df,   p=1
    ## Wald test            = 0  on 1 df,   p=1
    ## Score (logrank) test = 0  on 1 df,   p=1
    ICU.fitbyTroponinTmax <- coxph( Surv(Days, Status) ~ TroponinT_max, data = icu_patients_df1) 
    summary(ICU.fitbyTroponinTmax)
    ## Call:
    ## coxph(formula = Surv(Days, Status) ~ TroponinT_max, data = icu_patients_df1)
    ## 
    ##   n= 2061, number of events= 773 
    ## 
    ##                  coef exp(coef) se(coef)     z Pr(>|z|)   
    ## TroponinT_max 0.04152   1.04239  0.01583 2.623  0.00871 **
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ## 
    ##               exp(coef) exp(-coef) lower .95 upper .95
    ## TroponinT_max     1.042     0.9593     1.011     1.075
    ## 
    ## Concordance= 0.525  (se = 0.01 )
    ## Likelihood ratio test= 6  on 1 df,   p=0.01
    ## Wald test            = 6.88  on 1 df,   p=0.009
    ## Score (logrank) test = 6.89  on 1 df,   p=0.009
    # Urine_min
    ICU.fitbyUrinemin <- coxph( Surv(Days, Status) ~ Urine_min, data = icu_patients_df1) 
    summary(ICU.fitbyUrinemin)
    ## Call:
    ## coxph(formula = Surv(Days, Status) ~ Urine_min, data = icu_patients_df1)
    ## 
    ##   n= 2061, number of events= 773 
    ## 
    ##                 coef  exp(coef)   se(coef)      z Pr(>|z|)   
    ## Urine_min -0.0019252  0.9980767  0.0007179 -2.682  0.00733 **
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ## 
    ##           exp(coef) exp(-coef) lower .95 upper .95
    ## Urine_min    0.9981      1.002    0.9967    0.9995
    ## 
    ## Concordance= 0.525  (se = 0.01 )
    ## Likelihood ratio test= 8.51  on 1 df,   p=0.004
    ## Wald test            = 7.19  on 1 df,   p=0.007
    ## Score (logrank) test = 7.23  on 1 df,   p=0.007
    # WBC - min & max
    ICU.fitbyWBCmin <- coxph( Surv(Days, Status) ~ WBC_min, data = icu_patients_df1) 
    summary(ICU.fitbyWBCmin)
    ## Call:
    ## coxph(formula = Surv(Days, Status) ~ WBC_min, data = icu_patients_df1)
    ## 
    ##   n= 2061, number of events= 773 
    ## 
    ##             coef exp(coef) se(coef)     z Pr(>|z|)  
    ## WBC_min 0.009102  1.009144 0.004755 1.914   0.0556 .
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ## 
    ##         exp(coef) exp(-coef) lower .95 upper .95
    ## WBC_min     1.009     0.9909    0.9998     1.019
    ## 
    ## Concordance= 0.501  (se = 0.011 )
    ## Likelihood ratio test= 3.18  on 1 df,   p=0.07
    ## Wald test            = 3.66  on 1 df,   p=0.06
    ## Score (logrank) test = 3.59  on 1 df,   p=0.06
    ICU.fitbyWBCmax <- coxph( Surv(Days, Status) ~ WBC_max, data = icu_patients_df1) 
    summary(ICU.fitbyWBCmax)
    ## Call:
    ## coxph(formula = Surv(Days, Status) ~ WBC_max, data = icu_patients_df1)
    ## 
    ##   n= 2061, number of events= 773 
    ## 
    ##             coef exp(coef) se(coef)     z Pr(>|z|)
    ## WBC_max 0.003928  1.003936 0.004294 0.915     0.36
    ## 
    ##         exp(coef) exp(-coef) lower .95 upper .95
    ## WBC_max     1.004     0.9961    0.9955     1.012
    ## 
    ## Concordance= 0.491  (se = 0.011 )
    ## Likelihood ratio test= 0.79  on 1 df,   p=0.4
    ## Wald test            = 0.84  on 1 df,   p=0.4
    ## Score (logrank) test = 0.83  on 1 df,   p=0.4

    Univariable Cox model interpretation by Variable * Gender - non-significant log-rank test (p-value = 0.06), means that the null hypothesis of no difference in survival between genders is not rejected with a conclusion that survival does not significantly differ by gender. * ICUType - significant log-rank test (p-value close to 0), means that the null hypothesis is rejected with a conclusion that survival significantly differs by each ICU Type. Note that, hazard rate for those in Medical ICU is not statistically significantly different for those in Coronary Care Unit. * Length_of_stay - significant log-rank test (p-value close to 0), means that the null hypothesis is rejected with a conclusion that survival significantly differs by length of stay in hospital.For every additional day in hospital, the risk of mortality increases by approximately 1%. * Age - significant log-rank test (p-value close to 0), means that the null hypothesis is rejected with a conclusion that survival significantly differs by individual’s age. For every year older in age, the risk ofmortality increases by approcimately 3%. * Height - non-significant log-rank test (p-value = 0.1), means that the null hypothesis of no difference in survival for varying heights is not rejected with a conclusion that survival does not significantly differ by height. * Weight - the minimum, maximum and difference in weights as predictors result in significant log-rank tests indicating that the null hypothesis is rejected with a conclusion that survival significantly differs by weight. For every additional kilogram, the risk of mortality reduces by approximately 0.5-1%. Perhaps the use of a centred variable may make it easier to interpret. * SAPS1 - significant log-rank test (p-value close to 0), means that the null hypothesis is rejected with a conclusion that survival significantly differs by SAPS1 score. For every additional SAPS1 score, the risk of mortality increases by approximately 7%. * SOFA - significant log-rank test (p-value close to 0), means that the null hypothesis is rejected with a conclusion that survival significantly differs by SOFA score. For every additional SOFA score, the risk of mortality increases by approximately 6%. * Significant clinical measures are: * Bilirubin * Creatinine * FiO2 - maximum and difference from mean are significant * GCS - maximum and difference from mean are significant * HCO3 - difference from mean is highly significant, maximum and mean also significant * HR - difference from mean is significant * K - maximum and difference from mean are significant * MAP - minimum and difference from mean are significant * Na - minimum and difference from mean are significant * NISysABP
    * PaO2 * SysABP - maximum and difference from mean are significant * Temp * Urine * WBC - difference from mean is significant


    Updated list of significant log-ranks (5 May): ICUType, Age, Weight_max, Albumin_min, Bilirubin_max, BUN_max, Creatinine_max, Glucose_max, HCO3_min, K_max, Lactate_max, MAP_min, Na_min, NISysABP_min, NISysABP_max, pH_min, pH_max, RespRate_min, RespRate_max, Temp_min, Temp_max, TroponinT_max, Urine_min ***

    1. Fit an appropriate series of multivariable Cox proportional hazards models, justifying your approach. Assess each model you consider for goodness of fit and other relevant statistics.
    #################################################################################
    ### CODE COPIED TO TASK 1
    ## Create a dataset without missing or invalid data to use to build the model ##
    ## in order to remain consistent and allow comparisons between models to be made ##
    
    
    # # Check counts of missing data in each variable
    # for(i in 1:length(colnames(icu_patients_df1))){
    #   print(c(i,colnames(icu_patients_df1[i]), sum(is.na(icu_patients_df1[i]))))
    # }
    # ## Result: of the variables chosen to explore for the survival model, large amounts of missing data in:
    # ##         Height (992), NISysABP_min (453), NISysABP_max (453), Weight_max (146)
    # 
    # ## Decision: include Weight_max; remove Height, NISysABP_min, NISysABP_max
    # 
    # 
    # # Check counts of negative data (noted some -1 values) in each variable
    # for(i in 1:length(colnames(icu_patients_df1))){
    #   print(c(i,colnames(icu_patients_df1[i]), sum(icu_patients_df1[i] < 0)))
    # }
    # ## Result: negative values in Length_of_stay and SOFA (not listed in initial choice of variables anyway)
    
    
    # # Create a new dataset with the only non-missing data from list of initial variables chosen
    # # (excluding those with very high missingness i.e. Height, NISysABP_min, NISysABP_max)
    # nm_icu_model_df1 <- na.omit(subset(icu_patients_df1, 
    #                                    select=c(Days, Status, # the survival object variables
    #                                             RecordID, # keep record id for reference if needed
    #                                             in_hospital_death, # for task 1
    #                                             Age, Gender, ICUType, Weight_max,
    #                                             Albumin_min, Bilirubin_max,
    #                                             BUN_max, Creatinine_max, 
    #                                             GCS_max, Glucose_min, Glucose_max, 
    #                                             HCO3_min, HR_min, HR_max, K_min, 
    #                                             K_max, Lactate_max, MAP_min, Na_min,
    #                                             Na_max, Platelets_min, PFratio, pH_min,
    #                                             pH_max, RespRate_min, RespRate_max,
    #                                             Temp_min, Temp_max, TroponinT_max, 
    #                                             TroponinI_max, Urine_min, WBC_min, WBC_max)))
    
    ### CODE COPIED TO TASK 1
    #################################################################################
    ## Fitting multivariable models ##
    
    
    # Create a function to calculate AIC
    calc_aic <- function(model){
      # AIC = 2*k-2*logL (where k=df and df=number of coefficients in the model)
      AIC <- 2*length(model$coefficients)-2*model$loglik[2]
    }
    
    
    # Full model using all listed initial variables (excluding those with high missingness)
    ICU.mv_full <- coxph(Surv(Days, Status) ~ 
                        Age + Gender + ICUType + Weight_max + Albumin_min + Bilirubin_max +
                        BUN_max + Creatinine_max + GCS_max + Glucose_min + Glucose_max + 
                        HCO3_min + HR_min + HR_max + K_min + K_max + Lactate_max + MAP_min + 
                        Na_min + Na_max + Platelets_min + PFratio + pH_min + pH_max + 
                        RespRate_min + RespRate_max + Temp_min + Temp_max + TroponinT_max + 
                        TroponinI_max + Urine_min + WBC_min + WBC_max,
                        data = nm_icu_model_df1)
    summary(ICU.mv_full)
    ## Call:
    ## coxph(formula = Surv(Days, Status) ~ Age + Gender + ICUType + 
    ##     Weight_max + Albumin_min + Bilirubin_max + BUN_max + Creatinine_max + 
    ##     GCS_max + Glucose_min + Glucose_max + HCO3_min + HR_min + 
    ##     HR_max + K_min + K_max + Lactate_max + MAP_min + Na_min + 
    ##     Na_max + Platelets_min + PFratio + pH_min + pH_max + RespRate_min + 
    ##     RespRate_max + Temp_min + Temp_max + TroponinT_max + TroponinI_max + 
    ##     Urine_min + WBC_min + WBC_max, data = nm_icu_model_df1)
    ## 
    ##   n= 1915, number of events= 721 
    ## 
    ##                                             coef   exp(coef)    se(coef)      z
    ## Age                                   0.03317420  1.03373060  0.00293981 11.284
    ## GenderMale                           -0.02592987  0.97440342  0.08213299 -0.316
    ## ICUTypeCardiac Surgery Recovery Unit -0.77268237  0.46177276  0.16528997 -4.675
    ## ICUTypeMedical ICU                    0.31563031  1.37112327  0.11800531  2.675
    ## ICUTypeSurgical ICU                  -0.02301483  0.97724799  0.13801760 -0.167
    ## Weight_max                           -0.00243670  0.99756627  0.00193453 -1.260
    ## Albumin_min                          -0.11881877  0.88796872  0.06628328 -1.793
    ## Bilirubin_max                         0.01439740  1.01450154  0.00797465  1.805
    ## BUN_max                               0.01130860  1.01137279  0.00201088  5.624
    ## Creatinine_max                       -0.01482676  0.98528261  0.02766417 -0.536
    ## GCS_max                              -0.10623594  0.89921246  0.01452209 -7.315
    ## Glucose_min                          -0.00023802  0.99976201  0.00094230 -0.253
    ## Glucose_max                           0.00044814  1.00044824  0.00056329  0.796
    ## HCO3_min                              0.01886028  1.01903926  0.00968401  1.948
    ## HR_min                                0.00591389  1.00593141  0.00306191  1.931
    ## HR_max                                0.00202173  1.00202378  0.00200232  1.010
    ## K_min                                 0.06929166  1.07174875  0.08175841  0.848
    ## K_max                                -0.03279543  0.96773651  0.04629908 -0.708
    ## Lactate_max                           0.04373789  1.04470849  0.02026084  2.159
    ## MAP_min                              -0.00084711  0.99915325  0.00243055 -0.349
    ## Na_min                               -0.00760018  0.99242863  0.01840942 -0.413
    ## Na_max                               -0.03029393  0.97016034  0.01857343 -1.631
    ## Platelets_min                        -0.00033177  0.99966828  0.00042555 -0.780
    ## PFratio                              -0.00001688  0.99998312  0.00039515 -0.043
    ## pH_min                               -0.48286560  0.61701274  0.20067709 -2.406
    ## pH_max                                0.40316049  1.49654705  0.67511086  0.597
    ## RespRate_min                         -0.01676745  0.98337235  0.01305267 -1.285
    ## RespRate_max                          0.00762531  1.00765446  0.00620645  1.229
    ## Temp_min                             -0.04991242  0.95131273  0.04838417 -1.032
    ## Temp_max                             -0.13691486  0.87204447  0.05738362 -2.386
    ## TroponinT_max                         0.01708332  1.01723007  0.01829875  0.934
    ## TroponinI_max                         0.00253724  1.00254046  0.00399639  0.635
    ## Urine_min                            -0.00197615  0.99802581  0.00096945 -2.038
    ## WBC_min                               0.02549144  1.02581913  0.01460170  1.746
    ## WBC_max                              -0.01991114  0.98028578  0.01203181 -1.655
    ##                                                  Pr(>|z|)    
    ## Age                                  < 0.0000000000000002 ***
    ## GenderMale                                        0.75223    
    ## ICUTypeCardiac Surgery Recovery Unit    0.000002943718242 ***
    ## ICUTypeMedical ICU                                0.00748 ** 
    ## ICUTypeSurgical ICU                               0.86756    
    ## Weight_max                                        0.20782    
    ## Albumin_min                                       0.07304 .  
    ## Bilirubin_max                                     0.07101 .  
    ## BUN_max                                 0.000000018688704 ***
    ## Creatinine_max                                    0.59199    
    ## GCS_max                                 0.000000000000256 ***
    ## Glucose_min                                       0.80058    
    ## Glucose_max                                       0.42628    
    ## HCO3_min                                          0.05147 .  
    ## HR_min                                            0.05343 .  
    ## HR_max                                            0.31264    
    ## K_min                                             0.39671    
    ## K_max                                             0.47873    
    ## Lactate_max                                       0.03087 *  
    ## MAP_min                                           0.72744    
    ## Na_min                                            0.67972    
    ## Na_max                                            0.10288    
    ## Platelets_min                                     0.43561    
    ## PFratio                                           0.96592    
    ## pH_min                                            0.01612 *  
    ## pH_max                                            0.55039    
    ## RespRate_min                                      0.19893    
    ## RespRate_max                                      0.21922    
    ## Temp_min                                          0.30227    
    ## Temp_max                                          0.01703 *  
    ## TroponinT_max                                     0.35052    
    ## TroponinI_max                                     0.52550    
    ## Urine_min                                         0.04151 *  
    ## WBC_min                                           0.08085 .  
    ## WBC_max                                           0.09795 .  
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ## 
    ##                                      exp(coef) exp(-coef) lower .95 upper .95
    ## Age                                     1.0337     0.9674    1.0278    1.0397
    ## GenderMale                              0.9744     1.0263    0.8295    1.1446
    ## ICUTypeCardiac Surgery Recovery Unit    0.4618     2.1656    0.3340    0.6384
    ## ICUTypeMedical ICU                      1.3711     0.7293    1.0880    1.7279
    ## ICUTypeSurgical ICU                     0.9772     1.0233    0.7456    1.2808
    ## Weight_max                              0.9976     1.0024    0.9938    1.0014
    ## Albumin_min                             0.8880     1.1262    0.7798    1.0112
    ## Bilirubin_max                           1.0145     0.9857    0.9988    1.0305
    ## BUN_max                                 1.0114     0.9888    1.0074    1.0154
    ## Creatinine_max                          0.9853     1.0149    0.9333    1.0402
    ## GCS_max                                 0.8992     1.1121    0.8740    0.9252
    ## Glucose_min                             0.9998     1.0002    0.9979    1.0016
    ## Glucose_max                             1.0004     0.9996    0.9993    1.0016
    ## HCO3_min                                1.0190     0.9813    0.9999    1.0386
    ## HR_min                                  1.0059     0.9941    0.9999    1.0120
    ## HR_max                                  1.0020     0.9980    0.9981    1.0060
    ## K_min                                   1.0717     0.9331    0.9131    1.2580
    ## K_max                                   0.9677     1.0333    0.8838    1.0597
    ## Lactate_max                             1.0447     0.9572    1.0040    1.0870
    ## MAP_min                                 0.9992     1.0008    0.9944    1.0039
    ## Na_min                                  0.9924     1.0076    0.9573    1.0289
    ## Na_max                                  0.9702     1.0308    0.9355    1.0061
    ## Platelets_min                           0.9997     1.0003    0.9988    1.0005
    ## PFratio                                 1.0000     1.0000    0.9992    1.0008
    ## pH_min                                  0.6170     1.6207    0.4164    0.9143
    ## pH_max                                  1.4965     0.6682    0.3985    5.6201
    ## RespRate_min                            0.9834     1.0169    0.9585    1.0089
    ## RespRate_max                            1.0077     0.9924    0.9955    1.0200
    ## Temp_min                                0.9513     1.0512    0.8652    1.0459
    ## Temp_max                                0.8720     1.1467    0.7793    0.9759
    ## TroponinT_max                           1.0172     0.9831    0.9814    1.0544
    ## TroponinI_max                           1.0025     0.9975    0.9947    1.0104
    ## Urine_min                               0.9980     1.0020    0.9961    0.9999
    ## WBC_min                                 1.0258     0.9748    0.9969    1.0556
    ## WBC_max                                 0.9803     1.0201    0.9574    1.0037
    ## 
    ## Concordance= 0.743  (se = 0.009 )
    ## Likelihood ratio test= 518.5  on 35 df,   p=<0.0000000000000002
    ## Wald test            = 507.1  on 35 df,   p=<0.0000000000000002
    ## Score (logrank) test = 556  on 35 df,   p=<0.0000000000000002
    # Calculate full model AIC
    AIC.mv_full <- calc_aic(ICU.mv_full)
    AIC.mv_full #10136
    ## [1] 10135.95
    # 1st reduced model using all variables with significant log-rank tests
    ICU.mv_reduced1 <- coxph(Surv(Days, Status) ~
                            Age + ICUType + Weight_max + Albumin_min + Bilirubin_max +
                            BUN_max + Creatinine_max + Glucose_max + HCO3_min + 
                            K_max + Lactate_max + MAP_min + Na_min + pH_min + 
                            pH_max + RespRate_min + RespRate_max + Temp_min + 
                            Temp_max + TroponinT_max + Urine_min,
                            data = nm_icu_model_df1)
    summary(ICU.mv_reduced1)
    ## Call:
    ## coxph(formula = Surv(Days, Status) ~ Age + ICUType + Weight_max + 
    ##     Albumin_min + Bilirubin_max + BUN_max + Creatinine_max + 
    ##     Glucose_max + HCO3_min + K_max + Lactate_max + MAP_min + 
    ##     Na_min + pH_min + pH_max + RespRate_min + RespRate_max + 
    ##     Temp_min + Temp_max + TroponinT_max + Urine_min, data = nm_icu_model_df1)
    ## 
    ##   n= 1915, number of events= 721 
    ## 
    ##                                            coef  exp(coef)   se(coef)      z
    ## Age                                   0.0312354  1.0317284  0.0028364 11.012
    ## ICUTypeCardiac Surgery Recovery Unit -0.6478864  0.5231503  0.1526726 -4.244
    ## ICUTypeMedical ICU                    0.3901076  1.4771398  0.1174207  3.322
    ## ICUTypeSurgical ICU                   0.0838899  1.0875091  0.1335289  0.628
    ## Weight_max                           -0.0021849  0.9978175  0.0018229 -1.199
    ## Albumin_min                          -0.1540079  0.8572653  0.0645077 -2.387
    ## Bilirubin_max                         0.0144855  1.0145910  0.0081080  1.787
    ## BUN_max                               0.0123140  1.0123901  0.0019382  6.353
    ## Creatinine_max                       -0.0294390  0.9709901  0.0265352 -1.109
    ## Glucose_max                           0.0001531  1.0001531  0.0004043  0.379
    ## HCO3_min                              0.0174705  1.0176240  0.0092255  1.894
    ## K_max                                -0.0253362  0.9749821  0.0363475 -0.697
    ## Lactate_max                           0.0545008  1.0560134  0.0196475  2.774
    ## MAP_min                              -0.0012256  0.9987751  0.0023952 -0.512
    ## Na_min                               -0.0286393  0.9717669  0.0080801 -3.544
    ## pH_min                               -0.6275382  0.5339046  0.1968359 -3.188
    ## pH_max                                0.8969219  2.4520437  0.6400444  1.401
    ## RespRate_min                          0.0163537  1.0164882  0.0116422  1.405
    ## RespRate_max                          0.0124759  1.0125540  0.0056445  2.210
    ## Temp_min                             -0.0426614  0.9582358  0.0474244 -0.900
    ## Temp_max                             -0.0829817  0.9203680  0.0557570 -1.488
    ## TroponinT_max                         0.0168454  1.0169881  0.0175080  0.962
    ## Urine_min                            -0.0025723  0.9974311  0.0009526 -2.700
    ##                                                  Pr(>|z|)    
    ## Age                                  < 0.0000000000000002 ***
    ## ICUTypeCardiac Surgery Recovery Unit       0.000021992990 ***
    ## ICUTypeMedical ICU                               0.000893 ***
    ## ICUTypeSurgical ICU                              0.529838    
    ## Weight_max                                       0.230687    
    ## Albumin_min                                      0.016967 *  
    ## Bilirubin_max                                    0.074005 .  
    ## BUN_max                                    0.000000000211 ***
    ## Creatinine_max                                   0.267245    
    ## Glucose_max                                      0.704875    
    ## HCO3_min                                         0.058262 .  
    ## K_max                                            0.485769    
    ## Lactate_max                                      0.005538 ** 
    ## MAP_min                                          0.608865    
    ## Na_min                                           0.000393 ***
    ## pH_min                                           0.001432 ** 
    ## pH_max                                           0.161112    
    ## RespRate_min                                     0.160113    
    ## RespRate_max                                     0.027086 *  
    ## Temp_min                                         0.368351    
    ## Temp_max                                         0.136678    
    ## TroponinT_max                                    0.335972    
    ## Urine_min                                        0.006927 ** 
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ## 
    ##                                      exp(coef) exp(-coef) lower .95 upper .95
    ## Age                                     1.0317     0.9692    1.0260    1.0375
    ## ICUTypeCardiac Surgery Recovery Unit    0.5232     1.9115    0.3879    0.7056
    ## ICUTypeMedical ICU                      1.4771     0.6770    1.1735    1.8594
    ## ICUTypeSurgical ICU                     1.0875     0.9195    0.8371    1.4128
    ## Weight_max                              0.9978     1.0022    0.9943    1.0014
    ## Albumin_min                             0.8573     1.1665    0.7555    0.9728
    ## Bilirubin_max                           1.0146     0.9856    0.9986    1.0308
    ## BUN_max                                 1.0124     0.9878    1.0086    1.0162
    ## Creatinine_max                          0.9710     1.0299    0.9218    1.0228
    ## Glucose_max                             1.0002     0.9998    0.9994    1.0009
    ## HCO3_min                                1.0176     0.9827    0.9994    1.0362
    ## K_max                                   0.9750     1.0257    0.9079    1.0470
    ## Lactate_max                             1.0560     0.9470    1.0161    1.0975
    ## MAP_min                                 0.9988     1.0012    0.9941    1.0035
    ## Na_min                                  0.9718     1.0291    0.9565    0.9873
    ## pH_min                                  0.5339     1.8730    0.3630    0.7853
    ## pH_max                                  2.4520     0.4078    0.6994    8.5968
    ## RespRate_min                            1.0165     0.9838    0.9936    1.0399
    ## RespRate_max                            1.0126     0.9876    1.0014    1.0238
    ## Temp_min                                0.9582     1.0436    0.8732    1.0516
    ## Temp_max                                0.9204     1.0865    0.8251    1.0266
    ## TroponinT_max                           1.0170     0.9833    0.9827    1.0525
    ## Urine_min                               0.9974     1.0026    0.9956    0.9993
    ## 
    ## Concordance= 0.726  (se = 0.009 )
    ## Likelihood ratio test= 452.1  on 23 df,   p=<0.0000000000000002
    ## Wald test            = 439.8  on 23 df,   p=<0.0000000000000002
    ## Score (logrank) test = 482.2  on 23 df,   p=<0.0000000000000002
    # Calculate 1st reduced model AIC
    AIC.mv_reduced1 <- calc_aic(ICU.mv_reduced1)
    AIC.mv_reduced1 #10178
    ## [1] 10178.32
    # 2nd reduced model using all variables significant (using cut off p < 0.1) in ICU.mv_reduced1
    # (note using p < 0.1 gained better results than p < 0.05 as a cut off)
    ICU.mv_reduced2 <- coxph(Surv(Days, Status) ~
                            Age + ICUType + Albumin_min + Bilirubin_max + BUN_max + 
                            HCO3_min + Lactate_max + Na_min + pH_min + 
                            RespRate_max + Urine_min,
                            data = nm_icu_model_df1)
    summary(ICU.mv_reduced2)
    ## Call:
    ## coxph(formula = Surv(Days, Status) ~ Age + ICUType + Albumin_min + 
    ##     Bilirubin_max + BUN_max + HCO3_min + Lactate_max + Na_min + 
    ##     pH_min + RespRate_max + Urine_min, data = nm_icu_model_df1)
    ## 
    ##   n= 1915, number of events= 721 
    ## 
    ##                                            coef  exp(coef)   se(coef)      z
    ## Age                                   0.0336951  1.0342693  0.0026779 12.583
    ## ICUTypeCardiac Surgery Recovery Unit -0.7052417  0.4939891  0.1428496 -4.937
    ## ICUTypeMedical ICU                    0.3140214  1.3689190  0.1113657  2.820
    ## ICUTypeSurgical ICU                   0.0067186  1.0067412  0.1273610  0.053
    ## Albumin_min                          -0.1529698  0.8581556  0.0634725 -2.410
    ## Bilirubin_max                         0.0146272  1.0147347  0.0079423  1.842
    ## BUN_max                               0.0106532  1.0107102  0.0014018  7.600
    ## HCO3_min                              0.0173644  1.0175161  0.0087596  1.982
    ## Lactate_max                           0.0628071  1.0648214  0.0182291  3.445
    ## Na_min                               -0.0252732  0.9750435  0.0073066 -3.459
    ## pH_min                               -0.6409326  0.5268009  0.1946101 -3.293
    ## RespRate_max                          0.0143032  1.0144059  0.0047394  3.018
    ## Urine_min                            -0.0025693  0.9974340  0.0009383 -2.738
    ##                                                  Pr(>|z|)    
    ## Age                                  < 0.0000000000000002 ***
    ## ICUTypeCardiac Surgery Recovery Unit   0.0000007935243281 ***
    ## ICUTypeMedical ICU                               0.004806 ** 
    ## ICUTypeSurgical ICU                              0.957929    
    ## Albumin_min                                      0.015952 *  
    ## Bilirubin_max                                    0.065522 .  
    ## BUN_max                                0.0000000000000297 ***
    ## HCO3_min                                         0.047442 *  
    ## Lactate_max                                      0.000570 ***
    ## Na_min                                           0.000542 ***
    ## pH_min                                           0.000990 ***
    ## RespRate_max                                     0.002545 ** 
    ## Urine_min                                        0.006177 ** 
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ## 
    ##                                      exp(coef) exp(-coef) lower .95 upper .95
    ## Age                                     1.0343     0.9669    1.0289    1.0397
    ## ICUTypeCardiac Surgery Recovery Unit    0.4940     2.0243    0.3734    0.6536
    ## ICUTypeMedical ICU                      1.3689     0.7305    1.1005    1.7028
    ## ICUTypeSurgical ICU                     1.0067     0.9933    0.7843    1.2922
    ## Albumin_min                             0.8582     1.1653    0.7578    0.9718
    ## Bilirubin_max                           1.0147     0.9855    0.9991    1.0307
    ## BUN_max                                 1.0107     0.9894    1.0079    1.0135
    ## HCO3_min                                1.0175     0.9828    1.0002    1.0351
    ## Lactate_max                             1.0648     0.9391    1.0274    1.1036
    ## Na_min                                  0.9750     1.0256    0.9612    0.9891
    ## pH_min                                  0.5268     1.8983    0.3597    0.7714
    ## RespRate_max                            1.0144     0.9858    1.0050    1.0239
    ## Urine_min                               0.9974     1.0026    0.9956    0.9993
    ## 
    ## Concordance= 0.724  (se = 0.009 )
    ## Likelihood ratio test= 439.1  on 13 df,   p=<0.0000000000000002
    ## Wald test            = 422.9  on 13 df,   p=<0.0000000000000002
    ## Score (logrank) test = 457.6  on 13 df,   p=<0.0000000000000002
    # Calculate 2nd reduced model AIC
    AIC.mv_reduced2 <- calc_aic(ICU.mv_reduced2)
    AIC.mv_reduced2 #10171
    ## [1] 10171.34
    # 3rd reduced model by using step() function on the full model (which had the lowest AIC so far)
    ICU.mv_reduced3 <- step(ICU.mv_full, trace=1)
    ## Start:  AIC=10135.95
    ## Surv(Days, Status) ~ Age + Gender + ICUType + Weight_max + Albumin_min + 
    ##     Bilirubin_max + BUN_max + Creatinine_max + GCS_max + Glucose_min + 
    ##     Glucose_max + HCO3_min + HR_min + HR_max + K_min + K_max + 
    ##     Lactate_max + MAP_min + Na_min + Na_max + Platelets_min + 
    ##     PFratio + pH_min + pH_max + RespRate_min + RespRate_max + 
    ##     Temp_min + Temp_max + TroponinT_max + TroponinI_max + Urine_min + 
    ##     WBC_min + WBC_max
    ## 
    ##                  Df   AIC
    ## - PFratio         1 10134
    ## - Glucose_min     1 10134
    ## - Gender          1 10134
    ## - MAP_min         1 10134
    ## - Na_min          1 10134
    ## - Creatinine_max  1 10134
    ## - pH_max          1 10134
    ## - TroponinI_max   1 10134
    ## - K_max           1 10134
    ## - Platelets_min   1 10135
    ## - Glucose_max     1 10135
    ## - K_min           1 10135
    ## - TroponinT_max   1 10135
    ## - HR_max          1 10135
    ## - Temp_min        1 10135
    ## - RespRate_max    1 10135
    ## - Weight_max      1 10136
    ## - RespRate_min    1 10136
    ## <none>              10136
    ## - Na_max          1 10137
    ## - WBC_max         1 10137
    ## - Bilirubin_max   1 10137
    ## - WBC_min         1 10137
    ## - Albumin_min     1 10137
    ## - HCO3_min        1 10138
    ## - HR_min          1 10138
    ## - pH_min          1 10138
    ## - Lactate_max     1 10138
    ## - Urine_min       1 10139
    ## - Temp_max        1 10140
    ## - BUN_max         1 10163
    ## - GCS_max         1 10186
    ## - ICUType         3 10191
    ## - Age             1 10276
    ## 
    ## Step:  AIC=10133.95
    ## Surv(Days, Status) ~ Age + Gender + ICUType + Weight_max + Albumin_min + 
    ##     Bilirubin_max + BUN_max + Creatinine_max + GCS_max + Glucose_min + 
    ##     Glucose_max + HCO3_min + HR_min + HR_max + K_min + K_max + 
    ##     Lactate_max + MAP_min + Na_min + Na_max + Platelets_min + 
    ##     pH_min + pH_max + RespRate_min + RespRate_max + Temp_min + 
    ##     Temp_max + TroponinT_max + TroponinI_max + Urine_min + WBC_min + 
    ##     WBC_max
    ## 
    ##                  Df   AIC
    ## - Glucose_min     1 10132
    ## - Gender          1 10132
    ## - MAP_min         1 10132
    ## - Na_min          1 10132
    ## - Creatinine_max  1 10132
    ## - pH_max          1 10132
    ## - TroponinI_max   1 10132
    ## - K_max           1 10132
    ## - Platelets_min   1 10133
    ## - Glucose_max     1 10133
    ## - K_min           1 10133
    ## - TroponinT_max   1 10133
    ## - HR_max          1 10133
    ## - Temp_min        1 10133
    ## - RespRate_max    1 10133
    ## - Weight_max      1 10134
    ## - RespRate_min    1 10134
    ## <none>              10134
    ## - Na_max          1 10135
    ## - WBC_max         1 10135
    ## - Bilirubin_max   1 10135
    ## - WBC_min         1 10135
    ## - Albumin_min     1 10135
    ## - HCO3_min        1 10136
    ## - HR_min          1 10136
    ## - pH_min          1 10136
    ## - Lactate_max     1 10136
    ## - Urine_min       1 10137
    ## - Temp_max        1 10138
    ## - BUN_max         1 10162
    ## - GCS_max         1 10184
    ## - ICUType         3 10189
    ## - Age             1 10275
    ## 
    ## Step:  AIC=10132.02
    ## Surv(Days, Status) ~ Age + Gender + ICUType + Weight_max + Albumin_min + 
    ##     Bilirubin_max + BUN_max + Creatinine_max + GCS_max + Glucose_max + 
    ##     HCO3_min + HR_min + HR_max + K_min + K_max + Lactate_max + 
    ##     MAP_min + Na_min + Na_max + Platelets_min + pH_min + pH_max + 
    ##     RespRate_min + RespRate_max + Temp_min + Temp_max + TroponinT_max + 
    ##     TroponinI_max + Urine_min + WBC_min + WBC_max
    ## 
    ##                  Df   AIC
    ## - Gender          1 10130
    ## - MAP_min         1 10130
    ## - Na_min          1 10130
    ## - Creatinine_max  1 10130
    ## - pH_max          1 10130
    ## - TroponinI_max   1 10130
    ## - K_max           1 10130
    ## - Platelets_min   1 10131
    ## - Glucose_max     1 10131
    ## - K_min           1 10131
    ## - TroponinT_max   1 10131
    ## - HR_max          1 10131
    ## - Temp_min        1 10131
    ## - RespRate_max    1 10132
    ## - Weight_max      1 10132
    ## - RespRate_min    1 10132
    ## <none>              10132
    ## - Na_max          1 10133
    ## - WBC_max         1 10133
    ## - Bilirubin_max   1 10133
    ## - WBC_min         1 10133
    ## - Albumin_min     1 10133
    ## - HCO3_min        1 10134
    ## - HR_min          1 10134
    ## - pH_min          1 10134
    ## - Lactate_max     1 10134
    ## - Urine_min       1 10135
    ## - Temp_max        1 10136
    ## - BUN_max         1 10160
    ## - GCS_max         1 10182
    ## - ICUType         3 10187
    ## - Age             1 10273
    ## 
    ## Step:  AIC=10130.11
    ## Surv(Days, Status) ~ Age + ICUType + Weight_max + Albumin_min + 
    ##     Bilirubin_max + BUN_max + Creatinine_max + GCS_max + Glucose_max + 
    ##     HCO3_min + HR_min + HR_max + K_min + K_max + Lactate_max + 
    ##     MAP_min + Na_min + Na_max + Platelets_min + pH_min + pH_max + 
    ##     RespRate_min + RespRate_max + Temp_min + Temp_max + TroponinT_max + 
    ##     TroponinI_max + Urine_min + WBC_min + WBC_max
    ## 
    ##                  Df   AIC
    ## - MAP_min         1 10128
    ## - Na_min          1 10128
    ## - Creatinine_max  1 10128
    ## - pH_max          1 10128
    ## - K_max           1 10129
    ## - TroponinI_max   1 10129
    ## - Platelets_min   1 10129
    ## - K_min           1 10129
    ## - Glucose_max     1 10129
    ## - TroponinT_max   1 10129
    ## - HR_max          1 10129
    ## - Temp_min        1 10129
    ## - RespRate_max    1 10130
    ## - RespRate_min    1 10130
    ## <none>              10130
    ## - Weight_max      1 10130
    ## - WBC_max         1 10131
    ## - Na_max          1 10131
    ## - Bilirubin_max   1 10131
    ## - WBC_min         1 10131
    ## - Albumin_min     1 10132
    ## - HCO3_min        1 10132
    ## - HR_min          1 10132
    ## - pH_min          1 10132
    ## - Lactate_max     1 10133
    ## - Urine_min       1 10133
    ## - Temp_max        1 10134
    ## - BUN_max         1 10158
    ## - GCS_max         1 10180
    ## - ICUType         3 10185
    ## - Age             1 10271
    ## 
    ## Step:  AIC=10128.23
    ## Surv(Days, Status) ~ Age + ICUType + Weight_max + Albumin_min + 
    ##     Bilirubin_max + BUN_max + Creatinine_max + GCS_max + Glucose_max + 
    ##     HCO3_min + HR_min + HR_max + K_min + K_max + Lactate_max + 
    ##     Na_min + Na_max + Platelets_min + pH_min + pH_max + RespRate_min + 
    ##     RespRate_max + Temp_min + Temp_max + TroponinT_max + TroponinI_max + 
    ##     Urine_min + WBC_min + WBC_max
    ## 
    ##                  Df   AIC
    ## - Na_min          1 10126
    ## - Creatinine_max  1 10126
    ## - pH_max          1 10127
    ## - K_max           1 10127
    ## - TroponinI_max   1 10127
    ## - Platelets_min   1 10127
    ## - K_min           1 10127
    ## - Glucose_max     1 10127
    ## - TroponinT_max   1 10127
    ## - HR_max          1 10127
    ## - Temp_min        1 10127
    ## - RespRate_max    1 10128
    ## - RespRate_min    1 10128
    ## - Weight_max      1 10128
    ## <none>              10128
    ## - WBC_max         1 10129
    ## - Na_max          1 10129
    ## - Bilirubin_max   1 10129
    ## - WBC_min         1 10129
    ## - Albumin_min     1 10130
    ## - HCO3_min        1 10130
    ## - HR_min          1 10130
    ## - pH_min          1 10130
    ## - Lactate_max     1 10131
    ## - Urine_min       1 10131
    ## - Temp_max        1 10132
    ## - BUN_max         1 10156
    ## - GCS_max         1 10179
    ## - ICUType         3 10184
    ## - Age             1 10271
    ## 
    ## Step:  AIC=10126.46
    ## Surv(Days, Status) ~ Age + ICUType + Weight_max + Albumin_min + 
    ##     Bilirubin_max + BUN_max + Creatinine_max + GCS_max + Glucose_max + 
    ##     HCO3_min + HR_min + HR_max + K_min + K_max + Lactate_max + 
    ##     Na_max + Platelets_min + pH_min + pH_max + RespRate_min + 
    ##     RespRate_max + Temp_min + Temp_max + TroponinT_max + TroponinI_max + 
    ##     Urine_min + WBC_min + WBC_max
    ## 
    ##                  Df   AIC
    ## - K_max           1 10125
    ## - Creatinine_max  1 10125
    ## - pH_max          1 10125
    ## - K_min           1 10125
    ## - Platelets_min   1 10125
    ## - TroponinI_max   1 10125
    ## - TroponinT_max   1 10125
    ## - HR_max          1 10125
    ## - Glucose_max     1 10125
    ## - Temp_min        1 10126
    ## - RespRate_max    1 10126
    ## - RespRate_min    1 10126
    ## - Weight_max      1 10126
    ## <none>              10126
    ## - WBC_max         1 10127
    ## - WBC_min         1 10127
    ## - Bilirubin_max   1 10128
    ## - Albumin_min     1 10128
    ## - HCO3_min        1 10128
    ## - HR_min          1 10128
    ## - pH_min          1 10129
    ## - Lactate_max     1 10129
    ## - Urine_min       1 10130
    ## - Temp_max        1 10130
    ## - Na_max          1 10145
    ## - BUN_max         1 10154
    ## - GCS_max         1 10177
    ## - ICUType         3 10183
    ## - Age             1 10269
    ## 
    ## Step:  AIC=10124.71
    ## Surv(Days, Status) ~ Age + ICUType + Weight_max + Albumin_min + 
    ##     Bilirubin_max + BUN_max + Creatinine_max + GCS_max + Glucose_max + 
    ##     HCO3_min + HR_min + HR_max + K_min + Lactate_max + Na_max + 
    ##     Platelets_min + pH_min + pH_max + RespRate_min + RespRate_max + 
    ##     Temp_min + Temp_max + TroponinT_max + TroponinI_max + Urine_min + 
    ##     WBC_min + WBC_max
    ## 
    ##                  Df   AIC
    ## - K_min           1 10123
    ## - Creatinine_max  1 10123
    ## - pH_max          1 10123
    ## - Platelets_min   1 10123
    ## - TroponinI_max   1 10123
    ## - Glucose_max     1 10124
    ## - TroponinT_max   1 10124
    ## - HR_max          1 10124
    ## - Temp_min        1 10124
    ## - RespRate_max    1 10124
    ## - RespRate_min    1 10124
    ## - Weight_max      1 10125
    ## <none>              10125
    ## - WBC_max         1 10125
    ## - WBC_min         1 10126
    ## - Bilirubin_max   1 10126
    ## - Albumin_min     1 10126
    ## - HCO3_min        1 10126
    ## - HR_min          1 10127
    ## - pH_min          1 10127
    ## - Lactate_max     1 10127
    ## - Urine_min       1 10128
    ## - Temp_max        1 10129
    ## - Na_max          1 10143
    ## - BUN_max         1 10152
    ## - GCS_max         1 10175
    ## - ICUType         3 10182
    ## - Age             1 10268
    ## 
    ## Step:  AIC=10123
    ## Surv(Days, Status) ~ Age + ICUType + Weight_max + Albumin_min + 
    ##     Bilirubin_max + BUN_max + Creatinine_max + GCS_max + Glucose_max + 
    ##     HCO3_min + HR_min + HR_max + Lactate_max + Na_max + Platelets_min + 
    ##     pH_min + pH_max + RespRate_min + RespRate_max + Temp_min + 
    ##     Temp_max + TroponinT_max + TroponinI_max + Urine_min + WBC_min + 
    ##     WBC_max
    ## 
    ##                  Df   AIC
    ## - Creatinine_max  1 10121
    ## - pH_max          1 10121
    ## - Platelets_min   1 10121
    ## - TroponinI_max   1 10122
    ## - Glucose_max     1 10122
    ## - TroponinT_max   1 10122
    ## - HR_max          1 10122
    ## - Temp_min        1 10122
    ## - RespRate_max    1 10122
    ## - Weight_max      1 10123
    ## - RespRate_min    1 10123
    ## <none>              10123
    ## - WBC_max         1 10124
    ## - Bilirubin_max   1 10124
    ## - WBC_min         1 10124
    ## - Albumin_min     1 10124
    ## - HCO3_min        1 10125
    ## - HR_min          1 10125
    ## - pH_min          1 10125
    ## - Lactate_max     1 10125
    ## - Urine_min       1 10126
    ## - Temp_max        1 10127
    ## - Na_max          1 10143
    ## - BUN_max         1 10152
    ## - GCS_max         1 10174
    ## - ICUType         3 10184
    ## - Age             1 10268
    ## 
    ## Step:  AIC=10121.29
    ## Surv(Days, Status) ~ Age + ICUType + Weight_max + Albumin_min + 
    ##     Bilirubin_max + BUN_max + GCS_max + Glucose_max + HCO3_min + 
    ##     HR_min + HR_max + Lactate_max + Na_max + Platelets_min + 
    ##     pH_min + pH_max + RespRate_min + RespRate_max + Temp_min + 
    ##     Temp_max + TroponinT_max + TroponinI_max + Urine_min + WBC_min + 
    ##     WBC_max
    ## 
    ##                 Df   AIC
    ## - pH_max         1 10120
    ## - Platelets_min  1 10120
    ## - TroponinI_max  1 10120
    ## - Glucose_max    1 10120
    ## - TroponinT_max  1 10120
    ## - HR_max         1 10120
    ## - Temp_min       1 10120
    ## - RespRate_max   1 10120
    ## - RespRate_min   1 10121
    ## - Weight_max     1 10121
    ## <none>             10121
    ## - Bilirubin_max  1 10122
    ## - WBC_max        1 10122
    ## - Albumin_min    1 10123
    ## - WBC_min        1 10123
    ## - HCO3_min       1 10123
    ## - HR_min         1 10123
    ## - pH_min         1 10124
    ## - Lactate_max    1 10124
    ## - Urine_min      1 10124
    ## - Temp_max       1 10125
    ## - Na_max         1 10141
    ## - BUN_max        1 10165
    ## - GCS_max        1 10173
    ## - ICUType        3 10182
    ## - Age            1 10272
    ## 
    ## Step:  AIC=10119.7
    ## Surv(Days, Status) ~ Age + ICUType + Weight_max + Albumin_min + 
    ##     Bilirubin_max + BUN_max + GCS_max + Glucose_max + HCO3_min + 
    ##     HR_min + HR_max + Lactate_max + Na_max + Platelets_min + 
    ##     pH_min + RespRate_min + RespRate_max + Temp_min + Temp_max + 
    ##     TroponinT_max + TroponinI_max + Urine_min + WBC_min + WBC_max
    ## 
    ##                 Df   AIC
    ## - TroponinI_max  1 10118
    ## - Platelets_min  1 10118
    ## - Glucose_max    1 10118
    ## - TroponinT_max  1 10119
    ## - HR_max         1 10119
    ## - Temp_min       1 10119
    ## - RespRate_max   1 10119
    ## <none>             10120
    ## - RespRate_min   1 10120
    ## - Weight_max     1 10120
    ## - Bilirubin_max  1 10121
    ## - WBC_max        1 10121
    ## - Albumin_min    1 10121
    ## - WBC_min        1 10121
    ## - HR_min         1 10122
    ## - pH_min         1 10122
    ## - Lactate_max    1 10122
    ## - HCO3_min       1 10122
    ## - Urine_min      1 10122
    ## - Temp_max       1 10123
    ## - Na_max         1 10140
    ## - BUN_max        1 10163
    ## - GCS_max        1 10174
    ## - ICUType        3 10182
    ## - Age            1 10270
    ## 
    ## Step:  AIC=10118.15
    ## Surv(Days, Status) ~ Age + ICUType + Weight_max + Albumin_min + 
    ##     Bilirubin_max + BUN_max + GCS_max + Glucose_max + HCO3_min + 
    ##     HR_min + HR_max + Lactate_max + Na_max + Platelets_min + 
    ##     pH_min + RespRate_min + RespRate_max + Temp_min + Temp_max + 
    ##     TroponinT_max + Urine_min + WBC_min + WBC_max
    ## 
    ##                 Df   AIC
    ## - Platelets_min  1 10117
    ## - Glucose_max    1 10117
    ## - TroponinT_max  1 10117
    ## - Temp_min       1 10117
    ## - HR_max         1 10118
    ## <none>             10118
    ## - RespRate_min   1 10118
    ## - Weight_max     1 10118
    ## - RespRate_max   1 10118
    ## - Bilirubin_max  1 10119
    ## - WBC_max        1 10119
    ## - WBC_min        1 10119
    ## - Albumin_min    1 10120
    ## - HR_min         1 10120
    ## - pH_min         1 10120
    ## - Lactate_max    1 10120
    ## - Urine_min      1 10121
    ## - HCO3_min       1 10121
    ## - Temp_max       1 10122
    ## - Na_max         1 10138
    ## - BUN_max        1 10166
    ## - GCS_max        1 10172
    ## - ICUType        3 10181
    ## - Age            1 10268
    ## 
    ## Step:  AIC=10116.63
    ## Surv(Days, Status) ~ Age + ICUType + Weight_max + Albumin_min + 
    ##     Bilirubin_max + BUN_max + GCS_max + Glucose_max + HCO3_min + 
    ##     HR_min + HR_max + Lactate_max + Na_max + pH_min + RespRate_min + 
    ##     RespRate_max + Temp_min + Temp_max + TroponinT_max + Urine_min + 
    ##     WBC_min + WBC_max
    ## 
    ##                 Df   AIC
    ## - Glucose_max    1 10116
    ## - TroponinT_max  1 10116
    ## - Temp_min       1 10116
    ## - HR_max         1 10116
    ## <none>             10117
    ## - Weight_max     1 10117
    ## - RespRate_min   1 10117
    ## - RespRate_max   1 10117
    ## - WBC_min        1 10118
    ## - WBC_max        1 10118
    ## - Bilirubin_max  1 10118
    ## - HR_min         1 10118
    ## - Albumin_min    1 10118
    ## - pH_min         1 10119
    ## - Lactate_max    1 10119
    ## - Urine_min      1 10119
    ## - HCO3_min       1 10120
    ## - Temp_max       1 10120
    ## - Na_max         1 10136
    ## - BUN_max        1 10165
    ## - GCS_max        1 10171
    ## - ICUType        3 10180
    ## - Age            1 10268
    ## 
    ## Step:  AIC=10115.63
    ## Surv(Days, Status) ~ Age + ICUType + Weight_max + Albumin_min + 
    ##     Bilirubin_max + BUN_max + GCS_max + HCO3_min + HR_min + HR_max + 
    ##     Lactate_max + Na_max + pH_min + RespRate_min + RespRate_max + 
    ##     Temp_min + Temp_max + TroponinT_max + Urine_min + WBC_min + 
    ##     WBC_max
    ## 
    ##                 Df   AIC
    ## - TroponinT_max  1 10115
    ## - Temp_min       1 10115
    ## - HR_max         1 10115
    ## - Weight_max     1 10116
    ## <none>             10116
    ## - RespRate_max   1 10116
    ## - RespRate_min   1 10116
    ## - WBC_min        1 10116
    ## - WBC_max        1 10116
    ## - Bilirubin_max  1 10117
    ## - Albumin_min    1 10117
    ## - HR_min         1 10117
    ## - pH_min         1 10117
    ## - HCO3_min       1 10118
    ## - Urine_min      1 10118
    ## - Temp_max       1 10119
    ## - Lactate_max    1 10119
    ## - Na_max         1 10135
    ## - BUN_max        1 10164
    ## - GCS_max        1 10171
    ## - ICUType        3 10182
    ## - Age            1 10268
    ## 
    ## Step:  AIC=10114.75
    ## Surv(Days, Status) ~ Age + ICUType + Weight_max + Albumin_min + 
    ##     Bilirubin_max + BUN_max + GCS_max + HCO3_min + HR_min + HR_max + 
    ##     Lactate_max + Na_max + pH_min + RespRate_min + RespRate_max + 
    ##     Temp_min + Temp_max + Urine_min + WBC_min + WBC_max
    ## 
    ##                 Df   AIC
    ## - Temp_min       1 10114
    ## - HR_max         1 10114
    ## - Weight_max     1 10115
    ## <none>             10115
    ## - RespRate_min   1 10115
    ## - RespRate_max   1 10115
    ## - WBC_max        1 10116
    ## - WBC_min        1 10116
    ## - Albumin_min    1 10116
    ## - HR_min         1 10116
    ## - Bilirubin_max  1 10116
    ## - HCO3_min       1 10117
    ## - pH_min         1 10118
    ## - Urine_min      1 10118
    ## - Temp_max       1 10118
    ## - Lactate_max    1 10120
    ## - Na_max         1 10134
    ## - BUN_max        1 10163
    ## - GCS_max        1 10170
    ## - ICUType        3 10182
    ## - Age            1 10266
    ## 
    ## Step:  AIC=10113.91
    ## Surv(Days, Status) ~ Age + ICUType + Weight_max + Albumin_min + 
    ##     Bilirubin_max + BUN_max + GCS_max + HCO3_min + HR_min + HR_max + 
    ##     Lactate_max + Na_max + pH_min + RespRate_min + RespRate_max + 
    ##     Temp_max + Urine_min + WBC_min + WBC_max
    ## 
    ##                 Df   AIC
    ## - HR_max         1 10113
    ## <none>             10114
    ## - Weight_max     1 10114
    ## - RespRate_max   1 10114
    ## - RespRate_min   1 10114
    ## - WBC_min        1 10115
    ## - WBC_max        1 10115
    ## - HR_min         1 10115
    ## - Bilirubin_max  1 10115
    ## - Albumin_min    1 10115
    ## - HCO3_min       1 10116
    ## - pH_min         1 10117
    ## - Urine_min      1 10117
    ## - Lactate_max    1 10120
    ## - Temp_max       1 10120
    ## - Na_max         1 10133
    ## - BUN_max        1 10162
    ## - GCS_max        1 10170
    ## - ICUType        3 10180
    ## - Age            1 10265
    ## 
    ## Step:  AIC=10113.1
    ## Surv(Days, Status) ~ Age + ICUType + Weight_max + Albumin_min + 
    ##     Bilirubin_max + BUN_max + GCS_max + HCO3_min + HR_min + Lactate_max + 
    ##     Na_max + pH_min + RespRate_min + RespRate_max + Temp_max + 
    ##     Urine_min + WBC_min + WBC_max
    ## 
    ##                 Df   AIC
    ## <none>             10113
    ## - RespRate_min   1 10113
    ## - RespRate_max   1 10114
    ## - WBC_max        1 10114
    ## - Weight_max     1 10114
    ## - WBC_min        1 10114
    ## - Bilirubin_max  1 10114
    ## - Albumin_min    1 10115
    ## - HCO3_min       1 10115
    ## - pH_min         1 10116
    ## - Urine_min      1 10117
    ## - HR_min         1 10117
    ## - Temp_max       1 10119
    ## - Lactate_max    1 10120
    ## - Na_max         1 10132
    ## - BUN_max        1 10160
    ## - GCS_max        1 10169
    ## - ICUType        3 10182
    ## - Age            1 10265
    summary(ICU.mv_reduced3)
    ## Call:
    ## coxph(formula = Surv(Days, Status) ~ Age + ICUType + Weight_max + 
    ##     Albumin_min + Bilirubin_max + BUN_max + GCS_max + HCO3_min + 
    ##     HR_min + Lactate_max + Na_max + pH_min + RespRate_min + RespRate_max + 
    ##     Temp_max + Urine_min + WBC_min + WBC_max, data = nm_icu_model_df1)
    ## 
    ##   n= 1915, number of events= 721 
    ## 
    ##                                            coef  exp(coef)   se(coef)      z
    ## Age                                   0.0337030  1.0342774  0.0028800 11.703
    ## ICUTypeCardiac Surgery Recovery Unit -0.7585749  0.4683334  0.1455045 -5.213
    ## ICUTypeMedical ICU                    0.2665894  1.3055043  0.1118935  2.383
    ## ICUTypeSurgical ICU                  -0.0597760  0.9419755  0.1289216 -0.464
    ## Weight_max                           -0.0028717  0.9971324  0.0018165 -1.581
    ## Albumin_min                          -0.1217041  0.8854103  0.0647304 -1.880
    ## Bilirubin_max                         0.0151357  1.0152509  0.0078127  1.937
    ## BUN_max                               0.0108042  1.0108628  0.0014283  7.564
    ## GCS_max                              -0.1088301  0.8968828  0.0138841 -7.838
    ## HCO3_min                              0.0174338  1.0175867  0.0089639  1.945
    ## HR_min                                0.0064653  1.0064862  0.0026116  2.476
    ## Lactate_max                           0.0570025  1.0586585  0.0186807  3.051
    ## Na_max                               -0.0358594  0.9647759  0.0079585 -4.506
    ## pH_min                               -0.5088123  0.6012092  0.1823407 -2.790
    ## RespRate_min                         -0.0196914  0.9805013  0.0128529 -1.532
    ## RespRate_max                          0.0091086  1.0091502  0.0056285  1.618
    ## Temp_max                             -0.1436890  0.8661571  0.0527479 -2.724
    ## Urine_min                            -0.0020642  0.9979380  0.0009474 -2.179
    ## WBC_min                               0.0221331  1.0223798  0.0136925  1.616
    ## WBC_max                              -0.0178972  0.9822620  0.0114290 -1.566
    ##                                                  Pr(>|z|)    
    ## Age                                  < 0.0000000000000002 ***
    ## ICUTypeCardiac Surgery Recovery Unit  0.00000018539857563 ***
    ## ICUTypeMedical ICU                                0.01719 *  
    ## ICUTypeSurgical ICU                               0.64289    
    ## Weight_max                                        0.11391    
    ## Albumin_min                                       0.06008 .  
    ## Bilirubin_max                                     0.05271 .  
    ## BUN_max                               0.00000000000003898 ***
    ## GCS_max                               0.00000000000000456 ***
    ## HCO3_min                                          0.05179 .  
    ## HR_min                                            0.01330 *  
    ## Lactate_max                                       0.00228 ** 
    ## Na_max                                0.00000661319368369 ***
    ## pH_min                                            0.00526 ** 
    ## RespRate_min                                      0.12551    
    ## RespRate_max                                      0.10560    
    ## Temp_max                                          0.00645 ** 
    ## Urine_min                                         0.02934 *  
    ## WBC_min                                           0.10600    
    ## WBC_max                                           0.11736    
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ## 
    ##                                      exp(coef) exp(-coef) lower .95 upper .95
    ## Age                                     1.0343     0.9669    1.0285    1.0401
    ## ICUTypeCardiac Surgery Recovery Unit    0.4683     2.1352    0.3521    0.6229
    ## ICUTypeMedical ICU                      1.3055     0.7660    1.0484    1.6256
    ## ICUTypeSurgical ICU                     0.9420     1.0616    0.7316    1.2128
    ## Weight_max                              0.9971     1.0029    0.9936    1.0007
    ## Albumin_min                             0.8854     1.1294    0.7799    1.0052
    ## Bilirubin_max                           1.0153     0.9850    0.9998    1.0309
    ## BUN_max                                 1.0109     0.9893    1.0080    1.0137
    ## GCS_max                                 0.8969     1.1150    0.8728    0.9216
    ## HCO3_min                                1.0176     0.9827    0.9999    1.0356
    ## HR_min                                  1.0065     0.9936    1.0013    1.0117
    ## Lactate_max                             1.0587     0.9446    1.0206    1.0981
    ## Na_max                                  0.9648     1.0365    0.9498    0.9799
    ## pH_min                                  0.6012     1.6633    0.4205    0.8595
    ## RespRate_min                            0.9805     1.0199    0.9561    1.0055
    ## RespRate_max                            1.0092     0.9909    0.9981    1.0203
    ## Temp_max                                0.8662     1.1545    0.7811    0.9605
    ## Urine_min                               0.9979     1.0021    0.9961    0.9998
    ## WBC_min                                 1.0224     0.9781    0.9953    1.0502
    ## WBC_max                                 0.9823     1.0181    0.9605    1.0045
    ## 
    ## Concordance= 0.741  (se = 0.009 )
    ## Likelihood ratio test= 511.4  on 20 df,   p=<0.0000000000000002
    ## Wald test            = 497.9  on 20 df,   p=<0.0000000000000002
    ## Score (logrank) test = 541.4  on 20 df,   p=<0.0000000000000002
    ## Interestingly: GCS_max, HR_min & Na_max have worked their way back in (not significant on log-rank)
    
    # Calculate 3rd reduced model AIC
    AIC.mv_reduced3 <- calc_aic(ICU.mv_reduced3)
    AIC.mv_reduced3 #10113
    ## [1] 10113.1
    # 4th reduced model using significant variables (using cut off p < 0.1) from ICU.mv_reduced3 
    ICU.mv_reduced4 <- coxph(Surv(Days, Status) ~
                            Age + ICUType + Albumin_min + Bilirubin_max + BUN_max + 
                            GCS_max + HCO3_min + HR_min + Lactate_max + Na_max + 
                            pH_min + Temp_max + Urine_min,
                            data = nm_icu_model_df1)
    summary(ICU.mv_reduced4)
    ## Call:
    ## coxph(formula = Surv(Days, Status) ~ Age + ICUType + Albumin_min + 
    ##     Bilirubin_max + BUN_max + GCS_max + HCO3_min + HR_min + Lactate_max + 
    ##     Na_max + pH_min + Temp_max + Urine_min, data = nm_icu_model_df1)
    ## 
    ##   n= 1915, number of events= 721 
    ## 
    ##                                            coef  exp(coef)   se(coef)      z
    ## Age                                   0.0350388  1.0356599  0.0027689 12.654
    ## ICUTypeCardiac Surgery Recovery Unit -0.7506795  0.4720457  0.1436016 -5.228
    ## ICUTypeMedical ICU                    0.2966536  1.3453492  0.1113497  2.664
    ## ICUTypeSurgical ICU                  -0.0489970  0.9521840  0.1281524 -0.382
    ## Albumin_min                          -0.0975028  0.9070998  0.0640981 -1.521
    ## Bilirubin_max                         0.0176857  1.0178431  0.0075944  2.329
    ## BUN_max                               0.0103542  1.0104080  0.0013927  7.435
    ## GCS_max                              -0.1025152  0.9025644  0.0122724 -8.353
    ## HCO3_min                              0.0169520  1.0170965  0.0086722  1.955
    ## HR_min                                0.0064894  1.0065105  0.0025183  2.577
    ## Lactate_max                           0.0560927  1.0576957  0.0185001  3.032
    ## Na_max                               -0.0362758  0.9643743  0.0078693 -4.610
    ## pH_min                               -0.4684910  0.6259461  0.1892577 -2.475
    ## Temp_max                             -0.1537885  0.8574533  0.0518889 -2.964
    ## Urine_min                            -0.0019496  0.9980523  0.0009352 -2.085
    ##                                                  Pr(>|z|)    
    ## Age                                  < 0.0000000000000002 ***
    ## ICUTypeCardiac Surgery Recovery Unit    0.000000171804359 ***
    ## ICUTypeMedical ICU                                0.00772 ** 
    ## ICUTypeSurgical ICU                               0.70221    
    ## Albumin_min                                       0.12822    
    ## Bilirubin_max                                     0.01987 *  
    ## BUN_max                                 0.000000000000105 ***
    ## GCS_max                              < 0.0000000000000002 ***
    ## HCO3_min                                          0.05061 .  
    ## HR_min                                            0.00997 ** 
    ## Lactate_max                                       0.00243 ** 
    ## Na_max                                  0.000004031402074 ***
    ## pH_min                                            0.01331 *  
    ## Temp_max                                          0.00304 ** 
    ## Urine_min                                         0.03710 *  
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ## 
    ##                                      exp(coef) exp(-coef) lower .95 upper .95
    ## Age                                     1.0357     0.9656    1.0301    1.0413
    ## ICUTypeCardiac Surgery Recovery Unit    0.4720     2.1184    0.3562    0.6255
    ## ICUTypeMedical ICU                      1.3453     0.7433    1.0816    1.6735
    ## ICUTypeSurgical ICU                     0.9522     1.0502    0.7407    1.2241
    ## Albumin_min                             0.9071     1.1024    0.8000    1.0285
    ## Bilirubin_max                           1.0178     0.9825    1.0028    1.0331
    ## BUN_max                                 1.0104     0.9897    1.0077    1.0132
    ## GCS_max                                 0.9026     1.1080    0.8811    0.9245
    ## HCO3_min                                1.0171     0.9832    1.0000    1.0345
    ## HR_min                                  1.0065     0.9935    1.0016    1.0115
    ## Lactate_max                             1.0577     0.9455    1.0200    1.0968
    ## Na_max                                  0.9644     1.0369    0.9496    0.9794
    ## pH_min                                  0.6259     1.5976    0.4320    0.9071
    ## Temp_max                                0.8575     1.1662    0.7745    0.9492
    ## Urine_min                               0.9981     1.0020    0.9962    0.9999
    ## 
    ## Concordance= 0.738  (se = 0.009 )
    ## Likelihood ratio test= 501.6  on 15 df,   p=<0.0000000000000002
    ## Wald test            = 481.3  on 15 df,   p=<0.0000000000000002
    ## Score (logrank) test = 519.6  on 15 df,   p=<0.0000000000000002
    # Calculate 4th reduced model AIC
    AIC.mv_reduced4 <- calc_aic(ICU.mv_reduced4)
    AIC.mv_reduced4 #10112
    ## [1] 10112.83
    # Comparing models with LRT
    lapply(list(ICU.mv_reduced1, ICU.mv_reduced2, ICU.mv_reduced3, ICU.mv_reduced4), 
           function(reduced) {print(anova(ICU.mv_full, reduced))} )
    ## Analysis of Deviance Table
    ##  Cox model: response is  Surv(Days, Status)
    ##  Model 1: ~ Age + Gender + ICUType + Weight_max + Albumin_min + Bilirubin_max + BUN_max + Creatinine_max + GCS_max + Glucose_min + Glucose_max + HCO3_min + HR_min + HR_max + K_min + K_max + Lactate_max + MAP_min + Na_min + Na_max + Platelets_min + PFratio + pH_min + pH_max + RespRate_min + RespRate_max + Temp_min + Temp_max + TroponinT_max + TroponinI_max + Urine_min + WBC_min + WBC_max
    ##  Model 2: ~ Age + ICUType + Weight_max + Albumin_min + Bilirubin_max + BUN_max + Creatinine_max + Glucose_max + HCO3_min + K_max + Lactate_max + MAP_min + Na_min + pH_min + pH_max + RespRate_min + RespRate_max + Temp_min + Temp_max + TroponinT_max + Urine_min
    ##    loglik Chisq Df     P(>|Chi|)    
    ## 1 -5033.0                           
    ## 2 -5066.2 66.37 12 0.00000000152 ***
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ## Analysis of Deviance Table
    ##  Cox model: response is  Surv(Days, Status)
    ##  Model 1: ~ Age + Gender + ICUType + Weight_max + Albumin_min + Bilirubin_max + BUN_max + Creatinine_max + GCS_max + Glucose_min + Glucose_max + HCO3_min + HR_min + HR_max + K_min + K_max + Lactate_max + MAP_min + Na_min + Na_max + Platelets_min + PFratio + pH_min + pH_max + RespRate_min + RespRate_max + Temp_min + Temp_max + TroponinT_max + TroponinI_max + Urine_min + WBC_min + WBC_max
    ##  Model 2: ~ Age + ICUType + Albumin_min + Bilirubin_max + BUN_max + HCO3_min + Lactate_max + Na_min + pH_min + RespRate_max + Urine_min
    ##    loglik  Chisq Df     P(>|Chi|)    
    ## 1 -5033.0                            
    ## 2 -5072.7 79.388 22 0.00000002043 ***
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ## Analysis of Deviance Table
    ##  Cox model: response is  Surv(Days, Status)
    ##  Model 1: ~ Age + Gender + ICUType + Weight_max + Albumin_min + Bilirubin_max + BUN_max + Creatinine_max + GCS_max + Glucose_min + Glucose_max + HCO3_min + HR_min + HR_max + K_min + K_max + Lactate_max + MAP_min + Na_min + Na_max + Platelets_min + PFratio + pH_min + pH_max + RespRate_min + RespRate_max + Temp_min + Temp_max + TroponinT_max + TroponinI_max + Urine_min + WBC_min + WBC_max
    ##  Model 2: ~ Age + ICUType + Weight_max + Albumin_min + Bilirubin_max + BUN_max + GCS_max + HCO3_min + HR_min + Lactate_max + Na_max + pH_min + RespRate_min + RespRate_max + Temp_max + Urine_min + WBC_min + WBC_max
    ##    loglik  Chisq Df P(>|Chi|)
    ## 1 -5033.0                    
    ## 2 -5036.5 7.1483 15    0.9534
    ## Analysis of Deviance Table
    ##  Cox model: response is  Surv(Days, Status)
    ##  Model 1: ~ Age + Gender + ICUType + Weight_max + Albumin_min + Bilirubin_max + BUN_max + Creatinine_max + GCS_max + Glucose_min + Glucose_max + HCO3_min + HR_min + HR_max + K_min + K_max + Lactate_max + MAP_min + Na_min + Na_max + Platelets_min + PFratio + pH_min + pH_max + RespRate_min + RespRate_max + Temp_min + Temp_max + TroponinT_max + TroponinI_max + Urine_min + WBC_min + WBC_max
    ##  Model 2: ~ Age + ICUType + Albumin_min + Bilirubin_max + BUN_max + GCS_max + HCO3_min + HR_min + Lactate_max + Na_max + pH_min + Temp_max + Urine_min
    ##    loglik  Chisq Df P(>|Chi|)
    ## 1 -5033.0                    
    ## 2 -5041.4 16.877 20    0.6609
    ## [[1]]
    ## Analysis of Deviance Table
    ##  Cox model: response is  Surv(Days, Status)
    ##  Model 1: ~ Age + Gender + ICUType + Weight_max + Albumin_min + Bilirubin_max + BUN_max + Creatinine_max + GCS_max + Glucose_min + Glucose_max + HCO3_min + HR_min + HR_max + K_min + K_max + Lactate_max + MAP_min + Na_min + Na_max + Platelets_min + PFratio + pH_min + pH_max + RespRate_min + RespRate_max + Temp_min + Temp_max + TroponinT_max + TroponinI_max + Urine_min + WBC_min + WBC_max
    ##  Model 2: ~ Age + ICUType + Weight_max + Albumin_min + Bilirubin_max + BUN_max + Creatinine_max + Glucose_max + HCO3_min + K_max + Lactate_max + MAP_min + Na_min + pH_min + pH_max + RespRate_min + RespRate_max + Temp_min + Temp_max + TroponinT_max + Urine_min
    ##    loglik Chisq Df     P(>|Chi|)    
    ## 1 -5033.0                           
    ## 2 -5066.2 66.37 12 0.00000000152 ***
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ## 
    ## [[2]]
    ## Analysis of Deviance Table
    ##  Cox model: response is  Surv(Days, Status)
    ##  Model 1: ~ Age + Gender + ICUType + Weight_max + Albumin_min + Bilirubin_max + BUN_max + Creatinine_max + GCS_max + Glucose_min + Glucose_max + HCO3_min + HR_min + HR_max + K_min + K_max + Lactate_max + MAP_min + Na_min + Na_max + Platelets_min + PFratio + pH_min + pH_max + RespRate_min + RespRate_max + Temp_min + Temp_max + TroponinT_max + TroponinI_max + Urine_min + WBC_min + WBC_max
    ##  Model 2: ~ Age + ICUType + Albumin_min + Bilirubin_max + BUN_max + HCO3_min + Lactate_max + Na_min + pH_min + RespRate_max + Urine_min
    ##    loglik  Chisq Df     P(>|Chi|)    
    ## 1 -5033.0                            
    ## 2 -5072.7 79.388 22 0.00000002043 ***
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ## 
    ## [[3]]
    ## Analysis of Deviance Table
    ##  Cox model: response is  Surv(Days, Status)
    ##  Model 1: ~ Age + Gender + ICUType + Weight_max + Albumin_min + Bilirubin_max + BUN_max + Creatinine_max + GCS_max + Glucose_min + Glucose_max + HCO3_min + HR_min + HR_max + K_min + K_max + Lactate_max + MAP_min + Na_min + Na_max + Platelets_min + PFratio + pH_min + pH_max + RespRate_min + RespRate_max + Temp_min + Temp_max + TroponinT_max + TroponinI_max + Urine_min + WBC_min + WBC_max
    ##  Model 2: ~ Age + ICUType + Weight_max + Albumin_min + Bilirubin_max + BUN_max + GCS_max + HCO3_min + HR_min + Lactate_max + Na_max + pH_min + RespRate_min + RespRate_max + Temp_max + Urine_min + WBC_min + WBC_max
    ##    loglik  Chisq Df P(>|Chi|)
    ## 1 -5033.0                    
    ## 2 -5036.5 7.1483 15    0.9534
    ## 
    ## [[4]]
    ## Analysis of Deviance Table
    ##  Cox model: response is  Surv(Days, Status)
    ##  Model 1: ~ Age + Gender + ICUType + Weight_max + Albumin_min + Bilirubin_max + BUN_max + Creatinine_max + GCS_max + Glucose_min + Glucose_max + HCO3_min + HR_min + HR_max + K_min + K_max + Lactate_max + MAP_min + Na_min + Na_max + Platelets_min + PFratio + pH_min + pH_max + RespRate_min + RespRate_max + Temp_min + Temp_max + TroponinT_max + TroponinI_max + Urine_min + WBC_min + WBC_max
    ##  Model 2: ~ Age + ICUType + Albumin_min + Bilirubin_max + BUN_max + GCS_max + HCO3_min + HR_min + Lactate_max + Na_max + pH_min + Temp_max + Urine_min
    ##    loglik  Chisq Df P(>|Chi|)
    ## 1 -5033.0                    
    ## 2 -5041.4 16.877 20    0.6609
    ## Results: reduced1 and reduced2 - reject the null hypothesis that the reduced models are better (they are worse)
    ##          reduced3 and reduced4 - DONT reject the null hypothesis 
    ##                                    --> therefore the reduced models are better than the full model (matches our AICs)
    
    
    # Print the AICs all together to review
    aic_output <- c(AIC.mv_full, AIC.mv_reduced1, AIC.mv_reduced2, AIC.mv_reduced3, AIC.mv_reduced4)
    names(aic_output) <- c('Full AIC', 'Reduced 1 AIC', 'Reduced 2 AIC', 'Reduced 3 AIC', 'Reduced 4 AIC')
    print(aic_output)
    ##      Full AIC Reduced 1 AIC Reduced 2 AIC Reduced 3 AIC Reduced 4 AIC 
    ##      10135.95      10178.32      10171.34      10113.10      10112.83
    ## Decision: use ICU.mv_reduced4 as the provisional final model (lowest AIC and non-significant LRT)
    ## Note: the full model still has the largest (best) maximised log-likelihood, but we choose the simplified model for parsimony

    commentary

    ## Testing assumptions ##
    
    # Testing for proportional hazards assumption of ICU.mv_reduced4 using cox.zph()
    cox.zph(ICU.mv_reduced4, terms=FALSE)
    ##                                         chisq df              p
    ## Age                                   1.04471  1        0.30673
    ## ICUTypeCardiac Surgery Recovery Unit 10.34626  1        0.00130
    ## ICUTypeMedical ICU                    0.00654  1        0.93553
    ## ICUTypeSurgical ICU                   4.60886  1        0.03181
    ## Albumin_min                          12.67940  1        0.00037
    ## Bilirubin_max                        11.96366  1        0.00054
    ## BUN_max                               0.93552  1        0.33343
    ## GCS_max                              25.48016  1 0.000000446955
    ## HCO3_min                             25.17651  1 0.000000523154
    ## HR_min                                4.47650  1        0.03436
    ## Lactate_max                          32.07772  1 0.000000014813
    ## Na_max                                0.05096  1        0.82140
    ## pH_min                                0.41234  1        0.52078
    ## Temp_max                              1.89556  1        0.16858
    ## Urine_min                             3.24395  1        0.07169
    ## GLOBAL                               89.96094 15 0.000000000001
    ## Result: statistically significant global test, therefore the proportional hazards model is violated
    ##         (the variables that violate are: ICUType, Albumin_min, Bilirubin_max, GCS_max, HCO3_min, HR_min, Lactate_max)
    
    
    # Including time x covariate interactions to fix proportional hazards for problematic variables
    
    # Split the dataset at 90 days (~ 3 months)
    # Suspect there may be some systematic differences in patients who survive less than or greater than 3 months after ICU admission
    ICU.split <- survSplit(Surv(Days, Status) ~ ., data = nm_icu_model_df1, cut=c(90), episode= "tgroup", id="id2")
    head(ICU.split)
    ##   RecordID in_hospital_death Age Gender                       ICUType
    ## 1   132540                 0  76   Male Cardiac Surgery Recovery Unit
    ## 2   132540                 0  76   Male Cardiac Surgery Recovery Unit
    ## 3   132541                 0  44 Female                   Medical ICU
    ## 4   132541                 0  44 Female                   Medical ICU
    ## 5   132543                 0  68   Male                   Medical ICU
    ## 6   132543                 0  68   Male                   Medical ICU
    ##   Weight_max Albumin_min Bilirubin_max BUN_max Creatinine_max GCS_max
    ## 1       80.6         2.2           1.2      18            1.2      15
    ## 2       80.6         2.2           1.2      18            1.2      15
    ## 3       56.7         2.3           3.0       8            0.4       8
    ## 4       56.7         2.3           3.0       8            0.4       8
    ## 5       84.6         4.4           0.2      23            0.9      15
    ## 6       84.6         4.4           0.2      23            0.9      15
    ##   Glucose_min Glucose_max HCO3_min HR_min HR_max K_min K_max Lactate_max
    ## 1         105         105       21     80     88   4.3   4.3         2.9
    ## 2         105         105       21     80     88   4.3   4.3         2.9
    ## 3         119         141       24     57    113   3.3   8.6         1.9
    ## 4         119         141       24     57    113   3.3   8.6         1.9
    ## 5         106         129       27     57     88   4.0   4.2         1.2
    ## 6         106         129       27     57     88   4.0   4.2         1.2
    ##   MAP_min Na_min Na_max Platelets_min PFratio pH_min pH_max RespRate_min
    ## 1      43    139    139           164      89   7.34   7.45           11
    ## 2      43    139    139           164      89   7.34   7.45           11
    ## 3      71    137    140            72      65   7.51   7.51           18
    ## 4      71    137    140            72      65   7.51   7.51           18
    ## 5      72    140    141           315      64   7.47   7.51           12
    ## 6      72    140    141           315      64   7.47   7.51           12
    ##   RespRate_max Temp_min Temp_max TroponinT_max TroponinI_max Urine_min WBC_min
    ## 1           36     34.5     37.9          0.43          31.7         0     7.4
    ## 2           36     34.5     37.9          0.43          31.7         0     7.4
    ## 3           33     36.7     39.0          1.55          33.4        30     3.7
    ## 4           33     36.7     39.0          1.55          33.4        30     3.7
    ## 5           21     35.1     36.7          0.10           5.9       100     8.8
    ## 6           21     35.1     36.7          0.10           5.9       100     8.8
    ##   WBC_max id2 tstart Days Status tgroup
    ## 1    13.1   1      0   90      0      1
    ## 2    13.1   1     90 2408      0      2
    ## 3     4.2   2      0   90      0      1
    ## 4     4.2   2     90 2408      0      2
    ## 5    11.5   3      0   90      0      1
    ## 6    11.5   3     90  575      1      2
    # Fit the model with time x covariate interactions
    ICU.mv_reduced4.split <- coxph(Surv(Days, Status) ~
                                    Age + ICUType:strata(tgroup) + 
                                    Albumin_min:strata(tgroup) + 
                                    Bilirubin_max:strata(tgroup) + BUN_max + 
                                    GCS_max:strata(tgroup) + HCO3_min:strata(tgroup) + 
                                    HR_min:strata(tgroup) + 
                                    Lactate_max:strata(tgroup) + Na_max + pH_min + 
                                    Temp_max + Urine_min,
                                    data = ICU.split)
    summary(ICU.mv_reduced4.split)
    ## Call:
    ## coxph(formula = Surv(Days, Status) ~ Age + ICUType:strata(tgroup) + 
    ##     Albumin_min:strata(tgroup) + Bilirubin_max:strata(tgroup) + 
    ##     BUN_max + GCS_max:strata(tgroup) + HCO3_min:strata(tgroup) + 
    ##     HR_min:strata(tgroup) + Lactate_max:strata(tgroup) + Na_max + 
    ##     pH_min + Temp_max + Urine_min, data = ICU.split)
    ## 
    ##   n= 3448, number of events= 721 
    ## 
    ##                                                                   coef
    ## Age                                                          0.0346090
    ## BUN_max                                                      0.0102853
    ## Na_max                                                      -0.0373177
    ## pH_min                                                      -0.4234153
    ## Temp_max                                                    -0.1532807
    ## Urine_min                                                   -0.0018609
    ## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=1             0.0334824
    ## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=1 -1.1587488
    ## ICUTypeMedical ICU:strata(tgroup)tgroup=1                    0.1907664
    ## ICUTypeSurgical ICU:strata(tgroup)tgroup=1                          NA
    ## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=2             0.0755461
    ## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=2 -0.3034695
    ## ICUTypeMedical ICU:strata(tgroup)tgroup=2                    0.5346959
    ## ICUTypeSurgical ICU:strata(tgroup)tgroup=2                          NA
    ## strata(tgroup)tgroup=1:Albumin_min                          -0.2316071
    ## strata(tgroup)tgroup=2:Albumin_min                           0.0295442
    ## strata(tgroup)tgroup=1:Bilirubin_max                         0.0294162
    ## strata(tgroup)tgroup=2:Bilirubin_max                        -0.0166200
    ## strata(tgroup)tgroup=1:GCS_max                              -0.1284553
    ## strata(tgroup)tgroup=2:GCS_max                              -0.0686016
    ## strata(tgroup)tgroup=1:HCO3_min                             -0.0017832
    ## strata(tgroup)tgroup=2:HCO3_min                              0.0399073
    ## strata(tgroup)tgroup=1:HR_min                                0.0092707
    ## strata(tgroup)tgroup=2:HR_min                                0.0021339
    ## strata(tgroup)tgroup=1:Lactate_max                           0.0847352
    ## strata(tgroup)tgroup=2:Lactate_max                          -0.0122143
    ##                                                              exp(coef)
    ## Age                                                          1.0352149
    ## BUN_max                                                      1.0103384
    ## Na_max                                                       0.9633700
    ## pH_min                                                       0.6548066
    ## Temp_max                                                     0.8578889
    ## Urine_min                                                    0.9981409
    ## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=1             1.0340493
    ## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=1  0.3138787
    ## ICUTypeMedical ICU:strata(tgroup)tgroup=1                    1.2101767
    ## ICUTypeSurgical ICU:strata(tgroup)tgroup=1                          NA
    ## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=2             1.0784730
    ## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=2  0.7382524
    ## ICUTypeMedical ICU:strata(tgroup)tgroup=2                    1.7069291
    ## ICUTypeSurgical ICU:strata(tgroup)tgroup=2                          NA
    ## strata(tgroup)tgroup=1:Albumin_min                           0.7932578
    ## strata(tgroup)tgroup=2:Albumin_min                           1.0299849
    ## strata(tgroup)tgroup=1:Bilirubin_max                         1.0298531
    ## strata(tgroup)tgroup=2:Bilirubin_max                         0.9835173
    ## strata(tgroup)tgroup=1:GCS_max                               0.8794529
    ## strata(tgroup)tgroup=2:GCS_max                               0.9336986
    ## strata(tgroup)tgroup=1:HCO3_min                              0.9982184
    ## strata(tgroup)tgroup=2:HCO3_min                              1.0407143
    ## strata(tgroup)tgroup=1:HR_min                                1.0093138
    ## strata(tgroup)tgroup=2:HR_min                                1.0021362
    ## strata(tgroup)tgroup=1:Lactate_max                           1.0884289
    ## strata(tgroup)tgroup=2:Lactate_max                           0.9878600
    ##                                                               se(coef)      z
    ## Age                                                          0.0027578 12.550
    ## BUN_max                                                      0.0013839  7.432
    ## Na_max                                                       0.0078838 -4.733
    ## pH_min                                                       0.1948427 -2.173
    ## Temp_max                                                     0.0519571 -2.950
    ## Urine_min                                                    0.0009391 -1.982
    ## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=1             0.1693702  0.198
    ## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=1  0.2046760 -5.661
    ## ICUTypeMedical ICU:strata(tgroup)tgroup=1                    0.1313555  1.452
    ## ICUTypeSurgical ICU:strata(tgroup)tgroup=1                   0.0000000     NA
    ## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=2             0.1898386  0.398
    ## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=2  0.1780409 -1.704
    ## ICUTypeMedical ICU:strata(tgroup)tgroup=2                    0.1497039  3.572
    ## ICUTypeSurgical ICU:strata(tgroup)tgroup=2                   0.0000000     NA
    ## strata(tgroup)tgroup=1:Albumin_min                           0.0876911 -2.641
    ## strata(tgroup)tgroup=2:Albumin_min                           0.0932320  0.317
    ## strata(tgroup)tgroup=1:Bilirubin_max                         0.0081990  3.588
    ## strata(tgroup)tgroup=2:Bilirubin_max                         0.0176978 -0.939
    ## strata(tgroup)tgroup=1:GCS_max                               0.0157474 -8.157
    ## strata(tgroup)tgroup=2:GCS_max                               0.0190971 -3.592
    ## strata(tgroup)tgroup=1:HCO3_min                              0.0116061 -0.154
    ## strata(tgroup)tgroup=2:HCO3_min                              0.0122847  3.249
    ## strata(tgroup)tgroup=1:HR_min                                0.0032363  2.865
    ## strata(tgroup)tgroup=2:HR_min                                0.0038392  0.556
    ## strata(tgroup)tgroup=1:Lactate_max                           0.0205997  4.113
    ## strata(tgroup)tgroup=2:Lactate_max                           0.0345008 -0.354
    ##                                                                         Pr(>|z|)
    ## Age                                                         < 0.0000000000000002
    ## BUN_max                                                     0.000000000000107052
    ## Na_max                                                      0.000002207204558216
    ## pH_min                                                                  0.029772
    ## Temp_max                                                                0.003176
    ## Urine_min                                                               0.047532
    ## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=1                        0.843289
    ## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=1 0.000000015015891605
    ## ICUTypeMedical ICU:strata(tgroup)tgroup=1                               0.146421
    ## ICUTypeSurgical ICU:strata(tgroup)tgroup=1                                    NA
    ## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=2                        0.690668
    ## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=2             0.088289
    ## ICUTypeMedical ICU:strata(tgroup)tgroup=2                               0.000355
    ## ICUTypeSurgical ICU:strata(tgroup)tgroup=2                                    NA
    ## strata(tgroup)tgroup=1:Albumin_min                                      0.008262
    ## strata(tgroup)tgroup=2:Albumin_min                                      0.751328
    ## strata(tgroup)tgroup=1:Bilirubin_max                                    0.000334
    ## strata(tgroup)tgroup=2:Bilirubin_max                                    0.347680
    ## strata(tgroup)tgroup=1:GCS_max                              0.000000000000000343
    ## strata(tgroup)tgroup=2:GCS_max                                          0.000328
    ## strata(tgroup)tgroup=1:HCO3_min                                         0.877893
    ## strata(tgroup)tgroup=2:HCO3_min                                         0.001160
    ## strata(tgroup)tgroup=1:HR_min                                           0.004176
    ## strata(tgroup)tgroup=2:HR_min                                           0.578339
    ## strata(tgroup)tgroup=1:Lactate_max                          0.000038982884543304
    ## strata(tgroup)tgroup=2:Lactate_max                                      0.723318
    ##                                                                
    ## Age                                                         ***
    ## BUN_max                                                     ***
    ## Na_max                                                      ***
    ## pH_min                                                      *  
    ## Temp_max                                                    ** 
    ## Urine_min                                                   *  
    ## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=1               
    ## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=1 ***
    ## ICUTypeMedical ICU:strata(tgroup)tgroup=1                      
    ## ICUTypeSurgical ICU:strata(tgroup)tgroup=1                     
    ## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=2               
    ## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=2 .  
    ## ICUTypeMedical ICU:strata(tgroup)tgroup=2                   ***
    ## ICUTypeSurgical ICU:strata(tgroup)tgroup=2                     
    ## strata(tgroup)tgroup=1:Albumin_min                          ** 
    ## strata(tgroup)tgroup=2:Albumin_min                             
    ## strata(tgroup)tgroup=1:Bilirubin_max                        ***
    ## strata(tgroup)tgroup=2:Bilirubin_max                           
    ## strata(tgroup)tgroup=1:GCS_max                              ***
    ## strata(tgroup)tgroup=2:GCS_max                              ***
    ## strata(tgroup)tgroup=1:HCO3_min                                
    ## strata(tgroup)tgroup=2:HCO3_min                             ** 
    ## strata(tgroup)tgroup=1:HR_min                               ** 
    ## strata(tgroup)tgroup=2:HR_min                                  
    ## strata(tgroup)tgroup=1:Lactate_max                          ***
    ## strata(tgroup)tgroup=2:Lactate_max                             
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ## 
    ##                                                             exp(coef)
    ## Age                                                            1.0352
    ## BUN_max                                                        1.0103
    ## Na_max                                                         0.9634
    ## pH_min                                                         0.6548
    ## Temp_max                                                       0.8579
    ## Urine_min                                                      0.9981
    ## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=1               1.0340
    ## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=1    0.3139
    ## ICUTypeMedical ICU:strata(tgroup)tgroup=1                      1.2102
    ## ICUTypeSurgical ICU:strata(tgroup)tgroup=1                         NA
    ## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=2               1.0785
    ## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=2    0.7383
    ## ICUTypeMedical ICU:strata(tgroup)tgroup=2                      1.7069
    ## ICUTypeSurgical ICU:strata(tgroup)tgroup=2                         NA
    ## strata(tgroup)tgroup=1:Albumin_min                             0.7933
    ## strata(tgroup)tgroup=2:Albumin_min                             1.0300
    ## strata(tgroup)tgroup=1:Bilirubin_max                           1.0299
    ## strata(tgroup)tgroup=2:Bilirubin_max                           0.9835
    ## strata(tgroup)tgroup=1:GCS_max                                 0.8795
    ## strata(tgroup)tgroup=2:GCS_max                                 0.9337
    ## strata(tgroup)tgroup=1:HCO3_min                                0.9982
    ## strata(tgroup)tgroup=2:HCO3_min                                1.0407
    ## strata(tgroup)tgroup=1:HR_min                                  1.0093
    ## strata(tgroup)tgroup=2:HR_min                                  1.0021
    ## strata(tgroup)tgroup=1:Lactate_max                             1.0884
    ## strata(tgroup)tgroup=2:Lactate_max                             0.9879
    ##                                                             exp(-coef)
    ## Age                                                             0.9660
    ## BUN_max                                                         0.9898
    ## Na_max                                                          1.0380
    ## pH_min                                                          1.5272
    ## Temp_max                                                        1.1657
    ## Urine_min                                                       1.0019
    ## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=1                0.9671
    ## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=1     3.1859
    ## ICUTypeMedical ICU:strata(tgroup)tgroup=1                       0.8263
    ## ICUTypeSurgical ICU:strata(tgroup)tgroup=1                          NA
    ## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=2                0.9272
    ## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=2     1.3546
    ## ICUTypeMedical ICU:strata(tgroup)tgroup=2                       0.5858
    ## ICUTypeSurgical ICU:strata(tgroup)tgroup=2                          NA
    ## strata(tgroup)tgroup=1:Albumin_min                              1.2606
    ## strata(tgroup)tgroup=2:Albumin_min                              0.9709
    ## strata(tgroup)tgroup=1:Bilirubin_max                            0.9710
    ## strata(tgroup)tgroup=2:Bilirubin_max                            1.0168
    ## strata(tgroup)tgroup=1:GCS_max                                  1.1371
    ## strata(tgroup)tgroup=2:GCS_max                                  1.0710
    ## strata(tgroup)tgroup=1:HCO3_min                                 1.0018
    ## strata(tgroup)tgroup=2:HCO3_min                                 0.9609
    ## strata(tgroup)tgroup=1:HR_min                                   0.9908
    ## strata(tgroup)tgroup=2:HR_min                                   0.9979
    ## strata(tgroup)tgroup=1:Lactate_max                              0.9188
    ## strata(tgroup)tgroup=2:Lactate_max                              1.0123
    ##                                                             lower .95 upper .95
    ## Age                                                            1.0296    1.0408
    ## BUN_max                                                        1.0076    1.0131
    ## Na_max                                                         0.9486    0.9784
    ## pH_min                                                         0.4470    0.9593
    ## Temp_max                                                       0.7748    0.9499
    ## Urine_min                                                      0.9963    1.0000
    ## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=1               0.7419    1.4412
    ## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=1    0.2102    0.4688
    ## ICUTypeMedical ICU:strata(tgroup)tgroup=1                      0.9355    1.5655
    ## ICUTypeSurgical ICU:strata(tgroup)tgroup=1                         NA        NA
    ## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=2               0.7434    1.5646
    ## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=2    0.5208    1.0465
    ## ICUTypeMedical ICU:strata(tgroup)tgroup=2                      1.2729    2.2890
    ## ICUTypeSurgical ICU:strata(tgroup)tgroup=2                         NA        NA
    ## strata(tgroup)tgroup=1:Albumin_min                             0.6680    0.9420
    ## strata(tgroup)tgroup=2:Albumin_min                             0.8580    1.2365
    ## strata(tgroup)tgroup=1:Bilirubin_max                           1.0134    1.0465
    ## strata(tgroup)tgroup=2:Bilirubin_max                           0.9500    1.0182
    ## strata(tgroup)tgroup=1:GCS_max                                 0.8527    0.9070
    ## strata(tgroup)tgroup=2:GCS_max                                 0.8994    0.9693
    ## strata(tgroup)tgroup=1:HCO3_min                                0.9758    1.0212
    ## strata(tgroup)tgroup=2:HCO3_min                                1.0160    1.0661
    ## strata(tgroup)tgroup=1:HR_min                                  1.0029    1.0157
    ## strata(tgroup)tgroup=2:HR_min                                  0.9946    1.0097
    ## strata(tgroup)tgroup=1:Lactate_max                             1.0454    1.1333
    ## strata(tgroup)tgroup=2:Lactate_max                             0.9233    1.0570
    ## 
    ## Concordance= 0.748  (se = 0.009 )
    ## Likelihood ratio test= 564.7  on 24 df,   p=<0.0000000000000002
    ## Wald test            = 544.8  on 24 df,   p=<0.0000000000000002
    ## Score (logrank) test = 593.4  on 24 df,   p=<0.0000000000000002
    # evaluating the proportional hazards assumption again, for the model with time x covariate interactions
    cox.zph(ICU.mv_reduced4.split, terms=FALSE)
    ##                                                                chisq df      p
    ## Age                                                          0.16638  1 0.6833
    ## BUN_max                                                      0.02835  1 0.8663
    ## Na_max                                                       0.52712  1 0.4678
    ## pH_min                                                       0.20377  1 0.6517
    ## Temp_max                                                     0.36572  1 0.5453
    ## Urine_min                                                    1.64748  1 0.1993
    ## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=1             0.00282  1 0.9576
    ## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=1  0.68770  1 0.4069
    ## ICUTypeMedical ICU:strata(tgroup)tgroup=1                    0.00532  1 0.9419
    ## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=2             0.11821  1 0.7310
    ## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=2  2.10958  1 0.1464
    ## ICUTypeMedical ICU:strata(tgroup)tgroup=2                    0.58893  1 0.4428
    ## strata(tgroup)tgroup=1:Albumin_min                           2.32455  1 0.1273
    ## strata(tgroup)tgroup=2:Albumin_min                           0.00195  1 0.9648
    ## strata(tgroup)tgroup=1:Bilirubin_max                         0.92725  1 0.3356
    ## strata(tgroup)tgroup=2:Bilirubin_max                         3.38839  1 0.0657
    ## strata(tgroup)tgroup=1:GCS_max                              10.61588  1 0.0011
    ## strata(tgroup)tgroup=2:GCS_max                               2.53281  1 0.1115
    ## strata(tgroup)tgroup=1:HCO3_min                              4.83676  1 0.0279
    ## strata(tgroup)tgroup=2:HCO3_min                              1.56563  1 0.2108
    ## strata(tgroup)tgroup=1:HR_min                                0.97301  1 0.3239
    ## strata(tgroup)tgroup=2:HR_min                                0.32407  1 0.5692
    ## strata(tgroup)tgroup=1:Lactate_max                           5.00208  1 0.0253
    ## strata(tgroup)tgroup=2:Lactate_max                           5.91846  1 0.0150
    ## GLOBAL                                                      35.16653 24 0.0660
    ## Result: the global test is now insignificant (p = 0.07)
    
    
    # Checking Linearity by observing Martingale residuals
    
    # Refit the chosen model with any factor variables re-coded as numeric 
    # to allow the ggcoxfunctional() function to work
    ICU.mv_reduced4.nofactor <- coxph(Surv(Days, Status) ~
                                      Age + as.numeric(ICUType) + Albumin_min + Bilirubin_max + BUN_max + 
                                      GCS_max + HCO3_min + HR_min + Lactate_max + Na_max + 
                                      pH_min + Temp_max + Urine_min,
                                      data = nm_icu_model_df1)
    ggcoxfunctional(ICU.mv_reduced4.nofactor, nm_icu_model_df1)

    ## Result: they don't look particularly linear... especially with laboratory values very far from the reference ranges 
    ##         (likely few observations in this range / potential outliers)
    
    
    # Check linearity of the model as a whole
    ggcoxdiagnostics(ICU.mv_reduced4, type = "martingale", linear.predictions = FALSE, ggtheme = theme_bw()) 
    ## `geom_smooth()` using formula 'y ~ x'

    ## Result: appears reasonably linear with with 2 large negative outliers 
    ##         (large negative interpretation = 'lived too long')
    
    # Examine the observations with very large negative residuals (< -3)
    resid(ICU.mv_reduced4)[resid(ICU.mv_reduced4) < -3]
    ##      1511      1929 
    ## -4.197771 -3.207614
    icu_patients_df1[c(1511,1929),]
    ##      RecordID Length_of_stay SAPS1 SOFA Survival in_hospital_death Days Status
    ## 1511   136398             51    22   10       NA                 0 2408  FALSE
    ## 1929   137433             23    NA    7       NA                 0 2408  FALSE
    ##      Age Albumin_diff Albumin_max Albumin_min ALP_diff ALP_max ALP_min ALT_diff
    ## 1511  70    0.0186633         3.0         3.0 50.85204      45      74 105.4462
    ## 1929  78    0.6813367         2.3         2.3 57.14796     153     153 138.5538
    ##      ALT_max ALT_min AST_diff AST_max AST_min Bilirubin_diff Bilirubin_max
    ## 1511      40      15 151.3527      18      57       1.364039           0.9
    ## 1929     259     259 203.6473     373     373       4.935961           6.7
    ##      Bilirubin_min BUN_diff BUN_max BUN_min Cholesterol_diff Cholesterol_max
    ## 1511           0.4 99.47295     124     120         9.422764             147
    ## 1929           6.7 97.47295     122     122        81.422764              75
    ##      Cholesterol_min Creatinine_diff Creatinine_max Creatinine_min DiasABP_diff
    ## 1511             147        5.167554            6.4            5.8     11.54421
    ## 1929             101        2.967554            4.2            4.2           NA
    ##      DiasABP_max DiasABP_min FiO2_diff FiO2_max FiO2_min GCS_diff GCS_max
    ## 1511          67          47 0.4480799        1      0.4 6.244029       9
    ## 1929          NA          NA 0.4480799        1      1.0 3.755971      15
    ##      GCS_min Gender Glucose_diff Glucose_max Glucose_min HCO3_diff HCO3_max
    ## 1511       5 Female    142.14446         282          41 15.772548       10
    ## 1929      15   Male     66.85554          73          73  0.772548       22
    ##      HCO3_min  HCT_diff HCT_max HCT_min Height  HR_diff HR_max HR_min
    ## 1511        7 10.460129    31.5    20.5  165.1 45.07789     70     42
    ## 1929       22  4.760129    26.2    26.2  177.8 27.07789     65     60
    ##          ICUType    K_diff K_max K_min Lactate_diff Lactate_max Lactate_min
    ## 1511 Medical ICU 0.6352066   3.9   3.5     4.803596         7.6         7.6
    ## 1929 Medical ICU 0.1352066   4.0   4.0     2.203596         5.0         1.6
    ##       MAP_diff MAP_max MAP_min   Mg_diff Mg_max Mg_min  Na_diff Na_max Na_min
    ## 1511 120.23164     198      55 0.1842982    2.0    1.8 8.206607    133    131
    ## 1929  19.76836      58      65 0.6157018    2.6    2.6 6.206607    133    133
    ##      NIDiasABP_diff NIDiasABP_max NIDiasABP_min NIMAP_diff NIMAP_max NIMAP_min
    ## 1511       20.49101            72            37   21.38069     84.67     54.33
    ## 1929       31.49101            82            26   24.04069     93.00     51.67
    ##      NISysABP_diff NISysABP_max NISysABP_min PaCO2_diff PaCO2_max PaCO2_min
    ## 1511      37.69875          126           79  25.335797        22        15
    ## 1929      18.69875          119           98   4.335797        40        36
    ##      PaO2_diff PaO2_max PaO2_min    pH_diff pH_max pH_min Platelets_diff
    ## 1511  282.3821      441      120 0.14988624   7.31   7.22       77.76931
    ## 1929  108.6179      107       50 0.07988624   7.31   7.29      154.23069
    ##      Platelets_max Platelets_min RespRate_diff RespRate_max RespRate_min
    ## 1511           150           112      10.65142           30           10
    ## 1929           344           344      11.65142           31           17
    ##      SaO2_diff SaO2_max SaO2_min SysABP_diff SysABP_max SysABP_min Temp_diff
    ## 1511 0.7539211       98       98     42.3105        126         74  2.574083
    ## 1929 2.2460789       99       95          NA         NA         NA  1.174083
    ##      Temp_max Temp_min TroponinI_diff TroponinI_max TroponinI_min
    ## 1511     36.1     34.4       1.542945           3.9           3.9
    ## 1929     37.9     35.8       3.742945           3.9           1.7
    ##      TroponinT_diff TroponinT_max TroponinT_min Urine_diff Urine_max Urine_min
    ## 1511      0.6185006          0.27          0.05   99.21758        70         0
    ## 1929      3.3414994          4.01          1.67   99.21758       120         0
    ##       WBC_diff WBC_max WBC_min Weight_diff Weight_max Weight_min PFratio
    ## 1511 3.7331524     9.8     8.4    2.499878       78.2       78.2     120
    ## 1929 0.6668476    12.8    12.8    4.699878       76.0       76.0      50
    ## Interpretation: looks like they were relatively elderly with long lengths of stay
    ##                - one had low GCS values/high SAPS1/high lactate
    ##                - the other had high bilirubin/deranged LFTs/high lactate
    
    ## Decision: remove these outliers and re-fit the model to the dataset excluding these observations -->
    
    # Check the RecordIDs match up with the correct data in the non-missing, split dataset
    ICU.split[(ICU.split$RecordID == 136398 | ICU.split$RecordID == 137433),]
    ##      RecordID in_hospital_death Age Gender     ICUType Weight_max Albumin_min
    ## 2512   136398                 0  70 Female Medical ICU       78.2         3.0
    ## 2513   136398                 0  70 Female Medical ICU       78.2         3.0
    ## 3226   137433                 0  78   Male Medical ICU       76.0         2.3
    ## 3227   137433                 0  78   Male Medical ICU       76.0         2.3
    ##      Bilirubin_max BUN_max Creatinine_max GCS_max Glucose_min Glucose_max
    ## 2512           0.9     124            6.4       9          41         282
    ## 2513           0.9     124            6.4       9          41         282
    ## 3226           6.7     122            4.2      15          73          73
    ## 3227           6.7     122            4.2      15          73          73
    ##      HCO3_min HR_min HR_max K_min K_max Lactate_max MAP_min Na_min Na_max
    ## 2512        7     42     70   3.5   3.9         7.6      55    131    133
    ## 2513        7     42     70   3.5   3.9         7.6      55    131    133
    ## 3226       22     60     65   4.0   4.0         5.0      65    133    133
    ## 3227       22     60     65   4.0   4.0         5.0      65    133    133
    ##      Platelets_min PFratio pH_min pH_max RespRate_min RespRate_max Temp_min
    ## 2512           112     120   7.22   7.31           10           30     34.4
    ## 2513           112     120   7.22   7.31           10           30     34.4
    ## 3226           344      50   7.29   7.31           17           31     35.8
    ## 3227           344      50   7.29   7.31           17           31     35.8
    ##      Temp_max TroponinT_max TroponinI_max Urine_min WBC_min WBC_max  id2 tstart
    ## 2512     36.1          0.27           3.9         0     8.4     9.8 1400      0
    ## 2513     36.1          0.27           3.9         0     8.4     9.8 1400     90
    ## 3226     37.9          4.01           3.9         0    12.8    12.8 1792      0
    ## 3227     37.9          4.01           3.9         0    12.8    12.8 1792     90
    ##      Days Status tgroup
    ## 2512   90      0      1
    ## 2513 2408      0      2
    ## 3226   90      0      1
    ## 3227 2408      0      2
    # Remove these observations and save as new dataset
    ICU.split_noutliers <- ICU.split[!(ICU.split$RecordID %in% c(136398, 137433)),]
    
    # Refit the split model to the new dataset
    ICU.mv_reduced4.split.noutliers <- coxph(Surv(Days, Status) ~
                                              Age + ICUType:strata(tgroup) + 
                                              Albumin_min:strata(tgroup) + 
                                              Bilirubin_max:strata(tgroup) + BUN_max + 
                                              GCS_max:strata(tgroup) + HCO3_min:strata(tgroup) + 
                                              HR_min:strata(tgroup) + 
                                              Lactate_max:strata(tgroup) + Na_max + pH_min + 
                                              Temp_max + Urine_min,
                                              data = ICU.split_noutliers)
    summary(ICU.mv_reduced4.split.noutliers)
    ## Call:
    ## coxph(formula = Surv(Days, Status) ~ Age + ICUType:strata(tgroup) + 
    ##     Albumin_min:strata(tgroup) + Bilirubin_max:strata(tgroup) + 
    ##     BUN_max + GCS_max:strata(tgroup) + HCO3_min:strata(tgroup) + 
    ##     HR_min:strata(tgroup) + Lactate_max:strata(tgroup) + Na_max + 
    ##     pH_min + Temp_max + Urine_min, data = ICU.split_noutliers)
    ## 
    ##   n= 3444, number of events= 721 
    ## 
    ##                                                                   coef
    ## Age                                                          0.0345124
    ## BUN_max                                                      0.0111342
    ## Na_max                                                      -0.0404555
    ## pH_min                                                      -0.4124840
    ## Temp_max                                                    -0.1582918
    ## Urine_min                                                   -0.0019812
    ## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=1             0.0221166
    ## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=1 -1.1586329
    ## ICUTypeMedical ICU:strata(tgroup)tgroup=1                    0.2008633
    ## ICUTypeSurgical ICU:strata(tgroup)tgroup=1                          NA
    ## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=2             0.0655282
    ## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=2 -0.3071060
    ## ICUTypeMedical ICU:strata(tgroup)tgroup=2                    0.5463547
    ## ICUTypeSurgical ICU:strata(tgroup)tgroup=2                          NA
    ## strata(tgroup)tgroup=1:Albumin_min                          -0.2312474
    ## strata(tgroup)tgroup=2:Albumin_min                           0.0257121
    ## strata(tgroup)tgroup=1:Bilirubin_max                         0.0287543
    ## strata(tgroup)tgroup=2:Bilirubin_max                        -0.0159728
    ## strata(tgroup)tgroup=1:GCS_max                              -0.1281817
    ## strata(tgroup)tgroup=2:GCS_max                              -0.0686489
    ## strata(tgroup)tgroup=1:HCO3_min                             -0.0033246
    ## strata(tgroup)tgroup=2:HCO3_min                              0.0391071
    ## strata(tgroup)tgroup=1:HR_min                                0.0081504
    ## strata(tgroup)tgroup=2:HR_min                                0.0013052
    ## strata(tgroup)tgroup=1:Lactate_max                           0.0904054
    ## strata(tgroup)tgroup=2:Lactate_max                          -0.0013510
    ##                                                              exp(coef)
    ## Age                                                          1.0351149
    ## BUN_max                                                      1.0111965
    ## Na_max                                                       0.9603519
    ## pH_min                                                       0.6620038
    ## Temp_max                                                     0.8536006
    ## Urine_min                                                    0.9980208
    ## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=1             1.0223630
    ## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=1  0.3139150
    ## ICUTypeMedical ICU:strata(tgroup)tgroup=1                    1.2224577
    ## ICUTypeSurgical ICU:strata(tgroup)tgroup=1                          NA
    ## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=2             1.0677228
    ## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=2  0.7355726
    ## ICUTypeMedical ICU:strata(tgroup)tgroup=2                    1.7269462
    ## ICUTypeSurgical ICU:strata(tgroup)tgroup=2                          NA
    ## strata(tgroup)tgroup=1:Albumin_min                           0.7935431
    ## strata(tgroup)tgroup=2:Albumin_min                           1.0260455
    ## strata(tgroup)tgroup=1:Bilirubin_max                         1.0291717
    ## strata(tgroup)tgroup=2:Bilirubin_max                         0.9841541
    ## strata(tgroup)tgroup=1:GCS_max                               0.8796935
    ## strata(tgroup)tgroup=2:GCS_max                               0.9336545
    ## strata(tgroup)tgroup=1:HCO3_min                              0.9966809
    ## strata(tgroup)tgroup=2:HCO3_min                              1.0398819
    ## strata(tgroup)tgroup=1:HR_min                                1.0081837
    ## strata(tgroup)tgroup=2:HR_min                                1.0013060
    ## strata(tgroup)tgroup=1:Lactate_max                           1.0946180
    ## strata(tgroup)tgroup=2:Lactate_max                           0.9986499
    ##                                                               se(coef)      z
    ## Age                                                          0.0027499 12.550
    ## BUN_max                                                      0.0013776  8.082
    ## Na_max                                                       0.0078816 -5.133
    ## pH_min                                                       0.1978059 -2.085
    ## Temp_max                                                     0.0521644 -3.034
    ## Urine_min                                                    0.0009464 -2.093
    ## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=1             0.1694156  0.131
    ## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=1  0.2047092 -5.660
    ## ICUTypeMedical ICU:strata(tgroup)tgroup=1                    0.1311915  1.531
    ## ICUTypeSurgical ICU:strata(tgroup)tgroup=1                   0.0000000     NA
    ## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=2             0.1898951  0.345
    ## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=2  0.1780033 -1.725
    ## ICUTypeMedical ICU:strata(tgroup)tgroup=2                    0.1496993  3.650
    ## ICUTypeSurgical ICU:strata(tgroup)tgroup=2                   0.0000000     NA
    ## strata(tgroup)tgroup=1:Albumin_min                           0.0875372 -2.642
    ## strata(tgroup)tgroup=2:Albumin_min                           0.0932299  0.276
    ## strata(tgroup)tgroup=1:Bilirubin_max                         0.0081724  3.518
    ## strata(tgroup)tgroup=2:Bilirubin_max                         0.0173879 -0.919
    ## strata(tgroup)tgroup=1:GCS_max                               0.0157330 -8.147
    ## strata(tgroup)tgroup=2:GCS_max                               0.0190784 -3.598
    ## strata(tgroup)tgroup=1:HCO3_min                              0.0117341 -0.283
    ## strata(tgroup)tgroup=2:HCO3_min                              0.0123778  3.159
    ## strata(tgroup)tgroup=1:HR_min                                0.0032554  2.504
    ## strata(tgroup)tgroup=2:HR_min                                0.0038581  0.338
    ## strata(tgroup)tgroup=1:Lactate_max                           0.0202818  4.457
    ## strata(tgroup)tgroup=2:Lactate_max                           0.0342960 -0.039
    ##                                                                         Pr(>|z|)
    ## Age                                                         < 0.0000000000000002
    ## BUN_max                                                     0.000000000000000636
    ## Na_max                                                      0.000000285293278950
    ## pH_min                                                                  0.037042
    ## Temp_max                                                                0.002410
    ## Urine_min                                                               0.036316
    ## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=1                        0.896134
    ## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=1 0.000000015146402643
    ## ICUTypeMedical ICU:strata(tgroup)tgroup=1                               0.125752
    ## ICUTypeSurgical ICU:strata(tgroup)tgroup=1                                    NA
    ## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=2                        0.730037
    ## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=2             0.084477
    ## ICUTypeMedical ICU:strata(tgroup)tgroup=2                               0.000263
    ## ICUTypeSurgical ICU:strata(tgroup)tgroup=2                                    NA
    ## strata(tgroup)tgroup=1:Albumin_min                                      0.008249
    ## strata(tgroup)tgroup=2:Albumin_min                                      0.782708
    ## strata(tgroup)tgroup=1:Bilirubin_max                                    0.000434
    ## strata(tgroup)tgroup=2:Bilirubin_max                                    0.358295
    ## strata(tgroup)tgroup=1:GCS_max                              0.000000000000000372
    ## strata(tgroup)tgroup=2:GCS_max                                          0.000320
    ## strata(tgroup)tgroup=1:HCO3_min                                         0.776925
    ## strata(tgroup)tgroup=2:HCO3_min                                         0.001581
    ## strata(tgroup)tgroup=1:HR_min                                           0.012291
    ## strata(tgroup)tgroup=2:HR_min                                           0.735142
    ## strata(tgroup)tgroup=1:Lactate_max                          0.000008293318325089
    ## strata(tgroup)tgroup=2:Lactate_max                                      0.968577
    ##                                                                
    ## Age                                                         ***
    ## BUN_max                                                     ***
    ## Na_max                                                      ***
    ## pH_min                                                      *  
    ## Temp_max                                                    ** 
    ## Urine_min                                                   *  
    ## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=1               
    ## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=1 ***
    ## ICUTypeMedical ICU:strata(tgroup)tgroup=1                      
    ## ICUTypeSurgical ICU:strata(tgroup)tgroup=1                     
    ## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=2               
    ## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=2 .  
    ## ICUTypeMedical ICU:strata(tgroup)tgroup=2                   ***
    ## ICUTypeSurgical ICU:strata(tgroup)tgroup=2                     
    ## strata(tgroup)tgroup=1:Albumin_min                          ** 
    ## strata(tgroup)tgroup=2:Albumin_min                             
    ## strata(tgroup)tgroup=1:Bilirubin_max                        ***
    ## strata(tgroup)tgroup=2:Bilirubin_max                           
    ## strata(tgroup)tgroup=1:GCS_max                              ***
    ## strata(tgroup)tgroup=2:GCS_max                              ***
    ## strata(tgroup)tgroup=1:HCO3_min                                
    ## strata(tgroup)tgroup=2:HCO3_min                             ** 
    ## strata(tgroup)tgroup=1:HR_min                               *  
    ## strata(tgroup)tgroup=2:HR_min                                  
    ## strata(tgroup)tgroup=1:Lactate_max                          ***
    ## strata(tgroup)tgroup=2:Lactate_max                             
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ## 
    ##                                                             exp(coef)
    ## Age                                                            1.0351
    ## BUN_max                                                        1.0112
    ## Na_max                                                         0.9604
    ## pH_min                                                         0.6620
    ## Temp_max                                                       0.8536
    ## Urine_min                                                      0.9980
    ## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=1               1.0224
    ## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=1    0.3139
    ## ICUTypeMedical ICU:strata(tgroup)tgroup=1                      1.2225
    ## ICUTypeSurgical ICU:strata(tgroup)tgroup=1                         NA
    ## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=2               1.0677
    ## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=2    0.7356
    ## ICUTypeMedical ICU:strata(tgroup)tgroup=2                      1.7269
    ## ICUTypeSurgical ICU:strata(tgroup)tgroup=2                         NA
    ## strata(tgroup)tgroup=1:Albumin_min                             0.7935
    ## strata(tgroup)tgroup=2:Albumin_min                             1.0260
    ## strata(tgroup)tgroup=1:Bilirubin_max                           1.0292
    ## strata(tgroup)tgroup=2:Bilirubin_max                           0.9842
    ## strata(tgroup)tgroup=1:GCS_max                                 0.8797
    ## strata(tgroup)tgroup=2:GCS_max                                 0.9337
    ## strata(tgroup)tgroup=1:HCO3_min                                0.9967
    ## strata(tgroup)tgroup=2:HCO3_min                                1.0399
    ## strata(tgroup)tgroup=1:HR_min                                  1.0082
    ## strata(tgroup)tgroup=2:HR_min                                  1.0013
    ## strata(tgroup)tgroup=1:Lactate_max                             1.0946
    ## strata(tgroup)tgroup=2:Lactate_max                             0.9986
    ##                                                             exp(-coef)
    ## Age                                                             0.9661
    ## BUN_max                                                         0.9889
    ## Na_max                                                          1.0413
    ## pH_min                                                          1.5106
    ## Temp_max                                                        1.1715
    ## Urine_min                                                       1.0020
    ## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=1                0.9781
    ## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=1     3.1856
    ## ICUTypeMedical ICU:strata(tgroup)tgroup=1                       0.8180
    ## ICUTypeSurgical ICU:strata(tgroup)tgroup=1                          NA
    ## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=2                0.9366
    ## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=2     1.3595
    ## ICUTypeMedical ICU:strata(tgroup)tgroup=2                       0.5791
    ## ICUTypeSurgical ICU:strata(tgroup)tgroup=2                          NA
    ## strata(tgroup)tgroup=1:Albumin_min                              1.2602
    ## strata(tgroup)tgroup=2:Albumin_min                              0.9746
    ## strata(tgroup)tgroup=1:Bilirubin_max                            0.9717
    ## strata(tgroup)tgroup=2:Bilirubin_max                            1.0161
    ## strata(tgroup)tgroup=1:GCS_max                                  1.1368
    ## strata(tgroup)tgroup=2:GCS_max                                  1.0711
    ## strata(tgroup)tgroup=1:HCO3_min                                 1.0033
    ## strata(tgroup)tgroup=2:HCO3_min                                 0.9616
    ## strata(tgroup)tgroup=1:HR_min                                   0.9919
    ## strata(tgroup)tgroup=2:HR_min                                   0.9987
    ## strata(tgroup)tgroup=1:Lactate_max                              0.9136
    ## strata(tgroup)tgroup=2:Lactate_max                              1.0014
    ##                                                             lower .95 upper .95
    ## Age                                                            1.0296    1.0407
    ## BUN_max                                                        1.0085    1.0139
    ## Na_max                                                         0.9456    0.9753
    ## pH_min                                                         0.4492    0.9755
    ## Temp_max                                                       0.7706    0.9455
    ## Urine_min                                                      0.9962    0.9999
    ## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=1               0.7335    1.4250
    ## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=1    0.2102    0.4689
    ## ICUTypeMedical ICU:strata(tgroup)tgroup=1                      0.9453    1.5809
    ## ICUTypeSurgical ICU:strata(tgroup)tgroup=1                         NA        NA
    ## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=2               0.7359    1.5492
    ## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=2    0.5189    1.0427
    ## ICUTypeMedical ICU:strata(tgroup)tgroup=2                      1.2878    2.3158
    ## ICUTypeSurgical ICU:strata(tgroup)tgroup=2                         NA        NA
    ## strata(tgroup)tgroup=1:Albumin_min                             0.6684    0.9421
    ## strata(tgroup)tgroup=2:Albumin_min                             0.8547    1.2318
    ## strata(tgroup)tgroup=1:Bilirubin_max                           1.0128    1.0458
    ## strata(tgroup)tgroup=2:Bilirubin_max                           0.9512    1.0183
    ## strata(tgroup)tgroup=1:GCS_max                                 0.8530    0.9072
    ## strata(tgroup)tgroup=2:GCS_max                                 0.8994    0.9692
    ## strata(tgroup)tgroup=1:HCO3_min                                0.9740    1.0199
    ## strata(tgroup)tgroup=2:HCO3_min                                1.0150    1.0654
    ## strata(tgroup)tgroup=1:HR_min                                  1.0018    1.0146
    ## strata(tgroup)tgroup=2:HR_min                                  0.9938    1.0089
    ## strata(tgroup)tgroup=1:Lactate_max                             1.0520    1.1390
    ## strata(tgroup)tgroup=2:Lactate_max                             0.9337    1.0681
    ## 
    ## Concordance= 0.749  (se = 0.009 )
    ## Likelihood ratio test= 577.1  on 24 df,   p=<0.0000000000000002
    ## Wald test            = 558.2  on 24 df,   p=<0.0000000000000002
    ## Score (logrank) test = 607.6  on 24 df,   p=<0.0000000000000002
    # Calculate the split/no outlier model AIC
    AIC.mv_reduced4.split.noutliers <- calc_aic(ICU.mv_reduced4.split.noutliers)
    AIC.mv_reduced4.split.noutliers #10057 -- improvement
    ## [1] 10057.49
    ## Decision: use the 4th reduced model, split at time 3 months (90 days) on the split dataset with the outliers removed as the final dataset
    1. Present your final model. Your final model should not include all the predictor variables, just a small subset of them, which you have selected based on statistical significance and/or background knowledge.
    ICU.final.cox <- coxph(Surv(Days, Status) ~
                             Age + ICUType:strata(tgroup) + 
                             Albumin_min:strata(tgroup) + 
                             Bilirubin_max:strata(tgroup) + BUN_max + 
                             GCS_max:strata(tgroup) + HCO3_min:strata(tgroup) + 
                             HR_min:strata(tgroup) + Lactate_max:strata(tgroup) + 
                             Na_max + pH_min + Temp_max + Urine_min,
                             data = ICU.split_noutliers)
    summary(ICU.final.cox)
    ## Call:
    ## coxph(formula = Surv(Days, Status) ~ Age + ICUType:strata(tgroup) + 
    ##     Albumin_min:strata(tgroup) + Bilirubin_max:strata(tgroup) + 
    ##     BUN_max + GCS_max:strata(tgroup) + HCO3_min:strata(tgroup) + 
    ##     HR_min:strata(tgroup) + Lactate_max:strata(tgroup) + Na_max + 
    ##     pH_min + Temp_max + Urine_min, data = ICU.split_noutliers)
    ## 
    ##   n= 3444, number of events= 721 
    ## 
    ##                                                                   coef
    ## Age                                                          0.0345124
    ## BUN_max                                                      0.0111342
    ## Na_max                                                      -0.0404555
    ## pH_min                                                      -0.4124840
    ## Temp_max                                                    -0.1582918
    ## Urine_min                                                   -0.0019812
    ## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=1             0.0221166
    ## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=1 -1.1586329
    ## ICUTypeMedical ICU:strata(tgroup)tgroup=1                    0.2008633
    ## ICUTypeSurgical ICU:strata(tgroup)tgroup=1                          NA
    ## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=2             0.0655282
    ## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=2 -0.3071060
    ## ICUTypeMedical ICU:strata(tgroup)tgroup=2                    0.5463547
    ## ICUTypeSurgical ICU:strata(tgroup)tgroup=2                          NA
    ## strata(tgroup)tgroup=1:Albumin_min                          -0.2312474
    ## strata(tgroup)tgroup=2:Albumin_min                           0.0257121
    ## strata(tgroup)tgroup=1:Bilirubin_max                         0.0287543
    ## strata(tgroup)tgroup=2:Bilirubin_max                        -0.0159728
    ## strata(tgroup)tgroup=1:GCS_max                              -0.1281817
    ## strata(tgroup)tgroup=2:GCS_max                              -0.0686489
    ## strata(tgroup)tgroup=1:HCO3_min                             -0.0033246
    ## strata(tgroup)tgroup=2:HCO3_min                              0.0391071
    ## strata(tgroup)tgroup=1:HR_min                                0.0081504
    ## strata(tgroup)tgroup=2:HR_min                                0.0013052
    ## strata(tgroup)tgroup=1:Lactate_max                           0.0904054
    ## strata(tgroup)tgroup=2:Lactate_max                          -0.0013510
    ##                                                              exp(coef)
    ## Age                                                          1.0351149
    ## BUN_max                                                      1.0111965
    ## Na_max                                                       0.9603519
    ## pH_min                                                       0.6620038
    ## Temp_max                                                     0.8536006
    ## Urine_min                                                    0.9980208
    ## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=1             1.0223630
    ## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=1  0.3139150
    ## ICUTypeMedical ICU:strata(tgroup)tgroup=1                    1.2224577
    ## ICUTypeSurgical ICU:strata(tgroup)tgroup=1                          NA
    ## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=2             1.0677228
    ## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=2  0.7355726
    ## ICUTypeMedical ICU:strata(tgroup)tgroup=2                    1.7269462
    ## ICUTypeSurgical ICU:strata(tgroup)tgroup=2                          NA
    ## strata(tgroup)tgroup=1:Albumin_min                           0.7935431
    ## strata(tgroup)tgroup=2:Albumin_min                           1.0260455
    ## strata(tgroup)tgroup=1:Bilirubin_max                         1.0291717
    ## strata(tgroup)tgroup=2:Bilirubin_max                         0.9841541
    ## strata(tgroup)tgroup=1:GCS_max                               0.8796935
    ## strata(tgroup)tgroup=2:GCS_max                               0.9336545
    ## strata(tgroup)tgroup=1:HCO3_min                              0.9966809
    ## strata(tgroup)tgroup=2:HCO3_min                              1.0398819
    ## strata(tgroup)tgroup=1:HR_min                                1.0081837
    ## strata(tgroup)tgroup=2:HR_min                                1.0013060
    ## strata(tgroup)tgroup=1:Lactate_max                           1.0946180
    ## strata(tgroup)tgroup=2:Lactate_max                           0.9986499
    ##                                                               se(coef)      z
    ## Age                                                          0.0027499 12.550
    ## BUN_max                                                      0.0013776  8.082
    ## Na_max                                                       0.0078816 -5.133
    ## pH_min                                                       0.1978059 -2.085
    ## Temp_max                                                     0.0521644 -3.034
    ## Urine_min                                                    0.0009464 -2.093
    ## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=1             0.1694156  0.131
    ## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=1  0.2047092 -5.660
    ## ICUTypeMedical ICU:strata(tgroup)tgroup=1                    0.1311915  1.531
    ## ICUTypeSurgical ICU:strata(tgroup)tgroup=1                   0.0000000     NA
    ## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=2             0.1898951  0.345
    ## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=2  0.1780033 -1.725
    ## ICUTypeMedical ICU:strata(tgroup)tgroup=2                    0.1496993  3.650
    ## ICUTypeSurgical ICU:strata(tgroup)tgroup=2                   0.0000000     NA
    ## strata(tgroup)tgroup=1:Albumin_min                           0.0875372 -2.642
    ## strata(tgroup)tgroup=2:Albumin_min                           0.0932299  0.276
    ## strata(tgroup)tgroup=1:Bilirubin_max                         0.0081724  3.518
    ## strata(tgroup)tgroup=2:Bilirubin_max                         0.0173879 -0.919
    ## strata(tgroup)tgroup=1:GCS_max                               0.0157330 -8.147
    ## strata(tgroup)tgroup=2:GCS_max                               0.0190784 -3.598
    ## strata(tgroup)tgroup=1:HCO3_min                              0.0117341 -0.283
    ## strata(tgroup)tgroup=2:HCO3_min                              0.0123778  3.159
    ## strata(tgroup)tgroup=1:HR_min                                0.0032554  2.504
    ## strata(tgroup)tgroup=2:HR_min                                0.0038581  0.338
    ## strata(tgroup)tgroup=1:Lactate_max                           0.0202818  4.457
    ## strata(tgroup)tgroup=2:Lactate_max                           0.0342960 -0.039
    ##                                                                         Pr(>|z|)
    ## Age                                                         < 0.0000000000000002
    ## BUN_max                                                     0.000000000000000636
    ## Na_max                                                      0.000000285293278950
    ## pH_min                                                                  0.037042
    ## Temp_max                                                                0.002410
    ## Urine_min                                                               0.036316
    ## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=1                        0.896134
    ## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=1 0.000000015146402643
    ## ICUTypeMedical ICU:strata(tgroup)tgroup=1                               0.125752
    ## ICUTypeSurgical ICU:strata(tgroup)tgroup=1                                    NA
    ## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=2                        0.730037
    ## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=2             0.084477
    ## ICUTypeMedical ICU:strata(tgroup)tgroup=2                               0.000263
    ## ICUTypeSurgical ICU:strata(tgroup)tgroup=2                                    NA
    ## strata(tgroup)tgroup=1:Albumin_min                                      0.008249
    ## strata(tgroup)tgroup=2:Albumin_min                                      0.782708
    ## strata(tgroup)tgroup=1:Bilirubin_max                                    0.000434
    ## strata(tgroup)tgroup=2:Bilirubin_max                                    0.358295
    ## strata(tgroup)tgroup=1:GCS_max                              0.000000000000000372
    ## strata(tgroup)tgroup=2:GCS_max                                          0.000320
    ## strata(tgroup)tgroup=1:HCO3_min                                         0.776925
    ## strata(tgroup)tgroup=2:HCO3_min                                         0.001581
    ## strata(tgroup)tgroup=1:HR_min                                           0.012291
    ## strata(tgroup)tgroup=2:HR_min                                           0.735142
    ## strata(tgroup)tgroup=1:Lactate_max                          0.000008293318325089
    ## strata(tgroup)tgroup=2:Lactate_max                                      0.968577
    ##                                                                
    ## Age                                                         ***
    ## BUN_max                                                     ***
    ## Na_max                                                      ***
    ## pH_min                                                      *  
    ## Temp_max                                                    ** 
    ## Urine_min                                                   *  
    ## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=1               
    ## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=1 ***
    ## ICUTypeMedical ICU:strata(tgroup)tgroup=1                      
    ## ICUTypeSurgical ICU:strata(tgroup)tgroup=1                     
    ## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=2               
    ## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=2 .  
    ## ICUTypeMedical ICU:strata(tgroup)tgroup=2                   ***
    ## ICUTypeSurgical ICU:strata(tgroup)tgroup=2                     
    ## strata(tgroup)tgroup=1:Albumin_min                          ** 
    ## strata(tgroup)tgroup=2:Albumin_min                             
    ## strata(tgroup)tgroup=1:Bilirubin_max                        ***
    ## strata(tgroup)tgroup=2:Bilirubin_max                           
    ## strata(tgroup)tgroup=1:GCS_max                              ***
    ## strata(tgroup)tgroup=2:GCS_max                              ***
    ## strata(tgroup)tgroup=1:HCO3_min                                
    ## strata(tgroup)tgroup=2:HCO3_min                             ** 
    ## strata(tgroup)tgroup=1:HR_min                               *  
    ## strata(tgroup)tgroup=2:HR_min                                  
    ## strata(tgroup)tgroup=1:Lactate_max                          ***
    ## strata(tgroup)tgroup=2:Lactate_max                             
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ## 
    ##                                                             exp(coef)
    ## Age                                                            1.0351
    ## BUN_max                                                        1.0112
    ## Na_max                                                         0.9604
    ## pH_min                                                         0.6620
    ## Temp_max                                                       0.8536
    ## Urine_min                                                      0.9980
    ## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=1               1.0224
    ## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=1    0.3139
    ## ICUTypeMedical ICU:strata(tgroup)tgroup=1                      1.2225
    ## ICUTypeSurgical ICU:strata(tgroup)tgroup=1                         NA
    ## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=2               1.0677
    ## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=2    0.7356
    ## ICUTypeMedical ICU:strata(tgroup)tgroup=2                      1.7269
    ## ICUTypeSurgical ICU:strata(tgroup)tgroup=2                         NA
    ## strata(tgroup)tgroup=1:Albumin_min                             0.7935
    ## strata(tgroup)tgroup=2:Albumin_min                             1.0260
    ## strata(tgroup)tgroup=1:Bilirubin_max                           1.0292
    ## strata(tgroup)tgroup=2:Bilirubin_max                           0.9842
    ## strata(tgroup)tgroup=1:GCS_max                                 0.8797
    ## strata(tgroup)tgroup=2:GCS_max                                 0.9337
    ## strata(tgroup)tgroup=1:HCO3_min                                0.9967
    ## strata(tgroup)tgroup=2:HCO3_min                                1.0399
    ## strata(tgroup)tgroup=1:HR_min                                  1.0082
    ## strata(tgroup)tgroup=2:HR_min                                  1.0013
    ## strata(tgroup)tgroup=1:Lactate_max                             1.0946
    ## strata(tgroup)tgroup=2:Lactate_max                             0.9986
    ##                                                             exp(-coef)
    ## Age                                                             0.9661
    ## BUN_max                                                         0.9889
    ## Na_max                                                          1.0413
    ## pH_min                                                          1.5106
    ## Temp_max                                                        1.1715
    ## Urine_min                                                       1.0020
    ## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=1                0.9781
    ## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=1     3.1856
    ## ICUTypeMedical ICU:strata(tgroup)tgroup=1                       0.8180
    ## ICUTypeSurgical ICU:strata(tgroup)tgroup=1                          NA
    ## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=2                0.9366
    ## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=2     1.3595
    ## ICUTypeMedical ICU:strata(tgroup)tgroup=2                       0.5791
    ## ICUTypeSurgical ICU:strata(tgroup)tgroup=2                          NA
    ## strata(tgroup)tgroup=1:Albumin_min                              1.2602
    ## strata(tgroup)tgroup=2:Albumin_min                              0.9746
    ## strata(tgroup)tgroup=1:Bilirubin_max                            0.9717
    ## strata(tgroup)tgroup=2:Bilirubin_max                            1.0161
    ## strata(tgroup)tgroup=1:GCS_max                                  1.1368
    ## strata(tgroup)tgroup=2:GCS_max                                  1.0711
    ## strata(tgroup)tgroup=1:HCO3_min                                 1.0033
    ## strata(tgroup)tgroup=2:HCO3_min                                 0.9616
    ## strata(tgroup)tgroup=1:HR_min                                   0.9919
    ## strata(tgroup)tgroup=2:HR_min                                   0.9987
    ## strata(tgroup)tgroup=1:Lactate_max                              0.9136
    ## strata(tgroup)tgroup=2:Lactate_max                              1.0014
    ##                                                             lower .95 upper .95
    ## Age                                                            1.0296    1.0407
    ## BUN_max                                                        1.0085    1.0139
    ## Na_max                                                         0.9456    0.9753
    ## pH_min                                                         0.4492    0.9755
    ## Temp_max                                                       0.7706    0.9455
    ## Urine_min                                                      0.9962    0.9999
    ## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=1               0.7335    1.4250
    ## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=1    0.2102    0.4689
    ## ICUTypeMedical ICU:strata(tgroup)tgroup=1                      0.9453    1.5809
    ## ICUTypeSurgical ICU:strata(tgroup)tgroup=1                         NA        NA
    ## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=2               0.7359    1.5492
    ## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=2    0.5189    1.0427
    ## ICUTypeMedical ICU:strata(tgroup)tgroup=2                      1.2878    2.3158
    ## ICUTypeSurgical ICU:strata(tgroup)tgroup=2                         NA        NA
    ## strata(tgroup)tgroup=1:Albumin_min                             0.6684    0.9421
    ## strata(tgroup)tgroup=2:Albumin_min                             0.8547    1.2318
    ## strata(tgroup)tgroup=1:Bilirubin_max                           1.0128    1.0458
    ## strata(tgroup)tgroup=2:Bilirubin_max                           0.9512    1.0183
    ## strata(tgroup)tgroup=1:GCS_max                                 0.8530    0.9072
    ## strata(tgroup)tgroup=2:GCS_max                                 0.8994    0.9692
    ## strata(tgroup)tgroup=1:HCO3_min                                0.9740    1.0199
    ## strata(tgroup)tgroup=2:HCO3_min                                1.0150    1.0654
    ## strata(tgroup)tgroup=1:HR_min                                  1.0018    1.0146
    ## strata(tgroup)tgroup=2:HR_min                                  0.9938    1.0089
    ## strata(tgroup)tgroup=1:Lactate_max                             1.0520    1.1390
    ## strata(tgroup)tgroup=2:Lactate_max                             0.9337    1.0681
    ## 
    ## Concordance= 0.749  (se = 0.009 )
    ## Likelihood ratio test= 577.1  on 24 df,   p=<0.0000000000000002
    ## Wald test            = 558.2  on 24 df,   p=<0.0000000000000002
    ## Score (logrank) test = 607.6  on 24 df,   p=<0.0000000000000002
    1. For your final model, present a set of diagnostic statistics and/or charts and comment on them.

    2. Write a very brief paragraph summarising the most important findings of your final model. Include the most important values from the statistical output, and a simple clinical interpretation.

    Create your response to this task here, as a mixture of embedded (knitr) R code and any resulting outputs, and explanatory or commentary text.

    Save, knit and submit

    Reminder: don’t forget to save this file, to knit it to check that everything works, and then submit via the drop box in OpenLearning.

    Submit your assignment

    When you have finished, and are satisfied with your assignment solutions, and this file knits without errors and the output looks the way you want, then you should submit via the drop box in OpenLearning.

    Problems?

    If you encounter problems with any part of the process described above, please contact the course convenor via OpenLearning as soon as possible so that the issues can be resolved in good time, and well before the assignment is due.

    Additional Information

    Each task attracts the indicated number of marks (out of a total of 30 marks for the assignment). The instructions are deliberately open-ended and less prescriptive than the individual assignments to allow you some latitude in what you do and how you go about the task. However, to complete the tasks and gain full marks, you only need to replicate or repeat the steps covered in the course - if you do most or all of the things described in the revalant chapters of the HDAT9600 course, full marks will be awarded.

    Note also that with respect to the model fitting, there are no right or wrong answers when it comes to variable selection and other aspects of model specification. Deep understanding of the underlying medical concepts which govern patient treatment and outcomes in ICUs is not required or assumed, although you should try to gain some understanding of each variable using the links provided. You will not be marked down if your medical justifications are not exactly correct or complete, but do you best, and don’t hesitate to seek help from the course convenor.